suivi des signaux lors du Science Run 0 de XENONnT .

A.5 Estimation de la sensibilité de XENONnT pour la recherche de désintégration double beta sans émission de neutrino du 136 Xe . . . . . . . . . . . . .

List of Figures

1.1 Illustration of the general principle used to claim the observation of signal events. Data are represented in dotted orange points and compared to the expected energy spectrum from the background only hypothesis (solid blue). The signal expectation is represented by the solid red line, while the signal+background model is indicated by the dashed black line. . . . . . . [START_REF] Marrodán | Dark matter direct-detection experiments[END_REF] 1.2 Schematic of the main background sources for a rare event physic search experiments and some mitigation strategies associated to it. . . . . . . . . [START_REF] Workman | Review of Particle Physics[END_REF] 1. [START_REF] Dutta | Neutrino physics with dark matter detectors[END_REF] The measured residual muon fluxes in key underground facilities, which are consistent with predicted values (black line) from [START_REF] Mei | Muon-induced background study for underground laboratories[END_REF]. The sizes of the circles correspond to laboratory space by volume; red or blue denotes access by road tunnels or shafts, respectively.

Feynman diagram of NC leptonic weak interactions, with an exchange of a

Z 0 boson with a neutrino (a), or anti-neutrino (b). . . . . . . . . . . . . .

2.4

The probability that a particular neutrino mass state ν i with mass m i contains a particular charged lepton mass basis state (ν e , ν µ , ν τ ) is represented by colours. The left and right panels of the figure are referred to as normal or inverted mass squared ordering, respectively, referred to as NO or IO.

The value of the lightest neutrino mass is presently unknown.

2.6

Mass parabolas for nuclear isobars with even A. Due to the pairing term in the semi-empirical Bethe-Weizsäcker mass formula, even-even nuclei have lower masses than do odd-odd nuclei. Thus, β-decay is impossible from point a to point b, whereas in a second-order process, β -β -decay is energetically possible from point a to point c. Similarly, β + β + decay or doubleelectron capture decays can occur between point e and point c. 2.10 Theoretical electron energy distributions for 2νββ decay of 100 Mo to the ground state of 100 Ru obtained using the single-state dominance (SSD) and higher-state dominance (HSD) models [START_REF] Domin | Neutrino accompanied β ± β ± , β + /ec and ec/ec processes within single state dominance hypothesis[END_REF]. (a) Single-electron energies.

(b) Energy sum of two electrons. The single-electron energy spectra have a much more significant discriminating power. [START_REF] Ivan Esteban | The fate of hints: updated global analysis of three-flavor neutrino oscillations[END_REF]. The dashed violet horizontal band shows the upper limits on ⟨m ββ ⟩ obtained by KamLAND-Zen [START_REF] Abe | First Search for the Majorana Nature of Neutrinos in the Inverted Mass Ordering Region with KamLAND[END_REF]. Vertical lines refer to limit from cosmology [START_REF] Shouvik | Updated results on neutrino mass and mass hierarchy from cosmology with Planck 2018 likelihoods[END_REF] and KATRIN experiment [START_REF] Aker | Direct neutrino-mass measurement with sub-electronvolt sensitivity[END_REF], excluding part of the parameter spaces highlighted with gray bands.

2.14

Colourisation of Magellan images of the merging cluster 1E0657-558 (Bullet cluster), with overlay of mass distributions derived from X-ray spectroscopy made by the Chandra observatory [START_REF]NASA finds direct proof of dark matter[END_REF] in red, and from the gravitational lensing measurements [START_REF] Clowe | A direct empirical proof of the existence of dark matter[END_REF] in blue. Figure from [START_REF] Clowe | A direct empirical proof of the existence of dark matter[END_REF][START_REF]NASA finds direct proof of dark matter[END_REF]. . . . . . . . . . . .

Temperature power spectrum of the cosmic microwave background (CMB)

for a dark matter density contribution ΛCDM varying between 0.11 and and 0.43 (blue lines). All other input parameters of the model are kept constant. The dashed black lines shows the best fit to the Planck data from the 2018 release [START_REF] Aghanim | results[END_REF]. Small (large) multipoles l correspond to lange (small) angular scales: the main acoustic peak at l ∼ 200 is at ∼ 1 • ; l = 1800 corresponds to ∼ 0.1 • . Figure and caption from [START_REF] Schumann | Direct detection of WIMP dark matter: concepts and status[END_REF]. . . . . . . . . . .

2.16

Equilibrium (solid curve) and relic abundance (dashed curves) of WIMP particles, considering decreasing annihilation cross section ⟨σ A V⟩ scenario. [START_REF] Guido | Dark matter astrophysics[END_REF][START_REF] Kolb | The Early Universe[END_REF]. The x-axis (m/T) is the ratio between the WIMP mass, m, and the temperature, T , and it is proportional to the time starting from the Big Bang. . . . . . . . . . . . . . . . . . . . . . . . 2.17 Schematic of the three different approach considered for DM search. The signature of DM production from SM collision at collider, take the form of missing energy. The direct detection looks for signals of relic DM particles scattering off nuclei. The indirect search approach looks for DM annihilation signature from astrophysical objects. . . . . . . . . . . . . . . . . . . .

Figure and caption from

2.18

Nuclear recoil spectra induced by a m χ = 100 GeV WIMP in various common target materials, assuming a spin-independent WIMP-nucleon cross section σ SI = 1 × 10 -47 cm 2 . The rate for spin-independent interactions increases with A 2 , i.e., prefers heavy target materials. On the other hand, the rate for large nuclei (Xe, I, W) decreases at higher energies due to the form factor suppression. Figure and caption from [START_REF] Schumann | Direct detection of WIMP dark matter: concepts and status[END_REF]. . . . . . . . . . . .

2.19

Current best exclusion limits on the spin-independent DM-nucleon cross section as function of the DM particle mass (m χ ). The neutrino fog is depicted as function of the index n, with which a discovery limit scales with the number of background events, i.e, σ ∝ N -1/n . The neutrino fog is defined to be the regime for which n > 2. In purple the L-shaped beam for the neutron calibration composed by the guide and beam arms, pointing respectively towards the tank ceiling and the cryostat side wall. In red and green the two U-tubes surrounding the cryostat. Credit: XENON collaboration. . . . . . . . . . . . . . . . . . . . 4.1 Accumulated blinded data livetime acquired during the XENONnT first science run (SR0). The various colored bands represent periods of detector calibration with 220 Rn (blue), 83m Kr (orange), AmBe (green), 37 Ar (yellow) sources, or periods with operation conditions different than the nominal value for SR0 due to maintenance and hot-spot episode (grey) or alternative recirculation mode of the xenon purification system (violet). . . . . . . . . [START_REF] Wittweg | Second-Order Weak Decays in XENON1T and Future Xenon Time Projection Chambers[END_REF], with transition path from [START_REF] Manalaysay | Spatially uniform calibration of a liquid xenon detector at low energies using kr83m[END_REF] and updated half-life from [START_REF] Mccutchan | Nuclear data sheets for A = 83[END_REF]. . . . . . . . . . . . . . . . . . . .

Illustration of differents 83m

Kr events topologies reconstructed in XENONnT. lines from 83m Kr, 129m Xe, 131m Xe, and 37 Ar internal sources, to extract the g 1 and g 2 detector parameters. LYs and CYs measurements at higher energies from 12 C, 2 H, 40 K, and 60 Co, are shown as grey points but not considered for the linear fit due to non-optimal signal reconstruction and correction. A systematic uncertainty of 3% for the CY and 1% for the LY has been considered for all the points to account for the LY and CY variation observed during SR0. . . . . . . . . . . . . . . . . . . . . . . . . . [START_REF] Baha Balantekin | Fundamentals in Nuclear Physics: From Nuclear Structure to Cosmology[END_REF] 5.1 Top: Electronic recoil energy spectra for SS (blue) and MS (red) events in the central cylindrical 1 t fiducial volume of XENON1T. SS events with energies in the light blue shaded region marks around the 136 Xe Q ββ are blinded for the search for 0νββ decay. Black dashed line mark monoenergetic peaks and are labelled with the source isotopes. The fiducial volume selection leads to a lower rate of MS events at low energies while the increasing Compton-scattering cross-section leads to higher MS rate above ∽350 keV. Middle: Relative energy resolution for SS and MS events in XENON1T derived from the standard deviation σ(E r ) and mean µ(E r ) of Gaussian fits to mono-energetic lines. The data points are fitted with the empirical function from equation 5.1. Results from XENON100 [START_REF] Aprile | The XENON100 dark matter experiment[END_REF],

LUX [START_REF] Akerib | Signal yields, energy resolution, and recombination fluctuations in liquid xenon[END_REF], EXO-200 [START_REF] Anton | Search for neutrinoless double-β decay with the complete EXO-200 dataset[END_REF] and PandaX-II [START_REF] Ni | Searching for neutrino-less double beta decay of 136 Xe with PandaX-II liquid xenon detector[END_REF] are reported for comparison.

Bottom: Relative energy shift of the reconstructed µ(E r ) from the expected values E t for SS and MS events. Taken from [START_REF] Aprile | Energy resolution and linearity of XENON1T in the MeV energy range[END_REF]. . . . . . . . . . . 136 Xe energy spectrum with its associated uncertainties, based on the HSD theoretical spectrum from Kotila-Iachello. . . . . .

Final 2νββ decay of

5.22

Left: 8 B solar neutrino theoretical energy spectrum from [START_REF] Winter | The 8 B neutrino spectrum[END_REF] used as a primary inputs to compute the expected differential rate. Right: The ν e survival probability as function of the neutrino energy. Solar measurements of pp (red dot), 7 Be (blue dot), pep (cyan dot), and 8 B (green dots) from Borexino [START_REF] Agostini | Improved measurement of 8 B solar neutrinos with 1.5 kt • y of Borexino exposure[END_REF][START_REF] Bellini | Measurement of the solar 8 B neutrino rate with a liquid scintillator target and 3 mev energy threshold in the Borexino detector[END_REF][START_REF] Agostini | Experimental evidence of neutrinos produced in the CNO fusion cycle in the sun[END_REF][START_REF] Agostini | Comprehensive measurement of pp-chain solar neutrinos[END_REF]

5.26

Expected median sensitivity for the lower limit on the half-life of 136 Xe 0νββ decay for XENONnT derived from Asimov data [START_REF] Cowan | Asymptotic formulae for likelihood-based tests of new physics[END_REF] with its 1 σ statistical uncertainty. The projected sensitivity and the observed results from XENON1T, KamLAND-Zen [START_REF] Abe | First Search for the Majorana Nature of Neutrinos in the Inverted Mass Ordering Region with KamLAND[END_REF] and EXO-200 [START_REF] Anton | Search for neutrinoless double-β decay with the complete EXO-200 dataset[END_REF] The chapter 4 presents my contribution to analysis of data acquired during the first science run of XENONnT, from the 3rd of May, 2021, to the 4th of January, 2022. During this period, several calibrations of the detector were performed in order to characterize its response and correct for the detecor effects impacting the signal measurements, notably with a 83m Kr source, whose definition of selection criteria was under my responsability.

The stability of the measured signal at different energies during the whole science run has been studied by means of regular calibrations of the detector. This work has been performed within an analysis group that I coordinated.

A projection study of the sensitivity of XENONnT to the neutrinoless double beta decay search has been carried on in chapter 5, with a detailed description of the background and signal models whose implementation and study within the framework of the experiment was one of my main contributions and responsibility.

The conclusion of this manuscript offers a summary of the results of the work mentioned above and an outlook of the future perspectives regarding the neutrinoless double beta decay search with xenon dual-phase time projection chambers.

Introduction to new physics rare events searches

In the relentless quest to understand the nature and laws governing our Universe, one particular category of physical processes, characterized by an extremely rare occurrence, are promising probes to look for evidence of new physics beyond the Standard Model. The search for direct observation of rare event processes requires specific detection techniques to filter a weak signal out of an undesirable component of background events, so-called low-background experiments. Hereafter, we propose a general definition of those terms which encompasses the theme discussed in this work.

• A rare event is a scarce signal induced by a specific physical process with a peculiar signature. Order of few events over several years of experimental livetime are expected. By definition, such events seldom occur in the detection medium used to observe them. Within this category of events, we can highlight rare new physics processes never observed so far: in this work I will discuss the interactions of Dark Matter (DM) particles with the target's nuclei and the neutrinoless double beta (0νββ ) decay of a specific target nucleus isotope.

• A background event is produced by physical process that can mimic the signature of the rare event process sought. Such background events can limit the capacity of an experiment to detect, with a sufficiently high confidence level, the signal of interest. Therefore their comprehension and mitigation are critical in looking for 1

Chapter 1. Rare event physics searches rare event processes and will be further discussed in section 1.3.

• A low-background experiment is an experiment dedicated to the search for one or more rare event processes. Its primary constraint is to reduce the background noise as much as possible while maximizing its exposure1 , so to increase the probability of detecting a signal of interest. Various detection techniques fulfilling these requirements are used to search for rare physical processes and will be introduced in section 1.4. This thesis is performed in a low-background experiment called

XENONnT, which will be presented in detail in chapter 3.

By definition, background events have a signature very similar to the one from signals of interest thus a question arises:

How to be sure that an experiment really observed events from a rare physical process and not just backgrounds?

Deposited Energy

Arbitrary Unit Signal model

Background model

Signal + Background model By estimating all possible background sources relevant to the search for specific rare physical processes, one can compare the distribution of sensitive observables induced by signal-like events, to the corresponding ones from the background. This methods is illustrated in figure 1.1, where the observable used is the energy spectrum. It requires a good 1 1.2. The jewels of the rare event physics crown understanding of the background and signal response in the detector to build both models realistically. In the absence of positive evidence for signal observation, i.e., measurements that agree with the background-only hypothesis, we can derive an exclusion limit on the probability of the physical process to occur. Depending on the kind of process we are looking for, it translates into a limit on the cross-section in case of interaction or half-life in case of decay.

Measured spectrum

The jewels of the rare event physics crown

Many unanswered questions in physics require the study of rare processes. Among the most studied by the scientific community, we can mention the processes listed below that motivated most of the last decade's effort in rare event physics search.

• Neutrinos interactions, such as Coherent Elastic neutrino Nucleus Scattering (CEvNS) or neutrinos elastic scattering, are of particular interest to the understanding of this elusive particle properties but can also be used as a probe to study unreachable systems such as the core of nuclear power plant or the Sun. These interactions are allowed and predicted by the Standard Model (SM)2 of particle physics.

It is essential to notice that neutrino interactions while being an exciting signal to study, can be a source of background for the other rare processes mentioned here.

Therefore, they are discussed in more details in section 2.1.1.

• The quest for the first observation of Neutrinoless double beta decay is the cornerstone of this manuscript and will be adequately introduced in section 2.1.3.

Unlike the other processes mentioned above, this time, the rare event consists in a decay from a specific candidate isotope. Its detection is a potential indication of physics beyond the SM (BSM) and could also shed light on many unresolved problems in neutrino physics3 .

• Dark Matter direct detection is one of the most appealing goals in modern physics and would be an evidence of BSM physics. Dark matter is a key ingredient in the current understanding of our Universe, whose existence remains to be confirmed by direct detecting it. Its search motivated the development of the XENON program, whose XENONnT is the last generation of low-background experiments. to shield the detector from the cosmic-ray-induced particles, using the rock overburden as natural shielding. Muons are the most troublesome particles since they can penetrate deeply into the rock if they have sufficiently high energy. They can directly produce radiogenic isotope through spallation or induce secondary particles such as neutrons that could either interact in the detector or activate radiogenic isotopes in the materials, both cases being a source of background. However, muon flux decreases with energy, and thus the expected flux of muons decreases as the function of the depth. Several DUL were created worldwide using old mines or during the construction of tunnels.

External backgrounds

The environment surrounding the experiment 4 is a source of neutrons, γ or α, which represent a background for rare-events searches. They originate from muon interaction in the rock or natural radioactivity of the rock (γ-ray emission, β-, α-decays or spontaneous fission). Those particle fluxes can be efficiently shielded with high-Z material for charged particles and with hydrogen-rich materials for neutrons 5 . Two categories of shielding devices can be used, either passive shielding, such as Lead or Copper, whose only purpose is to stop the external backgrounds, or active shielding, like Cherenkov water tanks, which can be used as shielding and veto systems at the same time: this allows to reconstruct and subsequently reject background induced by particles that enter the detection medium. Usually, low-background experiments deploy multiple successive active/passive shielding systems to reduce external backgrounds to a negligible level, following the idea of Matryoshka dolls 6 , as illustrated in figure 1.2.

The second source of external background for rare event searches originates from the materials used to build the detector. Radionuclides are omnipresent in all raw materials, even at the trace level. Their presence is due to primordial radioactive contamina- 4 Rock and concrete in the underground laboratory. 5 Possibility to mix them with high neutron capture cross-section nuclei, like Gadolinium. 6 Set of wooden dolls of decreasing size placed one inside another. tion 7 , mostly of 238 U, 235 U and 232 Th decay chains and 40 K, but also anthropogenic radioactive contamination 8 , such as 137 Cs. The cosmogenic activation mentioned in the previous section can also produce radiogenic nuclides in the materials, like 60 Co.

This source of background is one of the most difficult to mitigate due to its proximity to the detection medium. A careful selection of the most radio-pure material is a mandatory step for all low-background experiments. Furthermore, it is necessary to know the materials contamination levels accurately to estimate the resulting components of the total background model. This is done through dedicated screening measurements of different samples of the materials used to build the experiment. The isotopic composition of materials and the specific activities of radionuclides were measured through two complementary techniques: γ-ray spectroscopy and mass spectroscopy, employing high-purity 7 Radionuclides that have existed in their current form since before Earth was formed. They are residuals from the Big Bang, cosmogenic sources, and ancient supernovae explosions that occurred before the formation of the solar system. 8 Caused by humans activities like nuclear explosions residual's in the atmosphere, radioactive leakages by nuclear power plants and radioactive isotopes used in industries.

1

Chapter 1. Rare event physics searches Germanium detectors (HPGe), and inductive coupled plasma mass spectrometer (ICP-MS), respectively 9 . These screening techniques can reach sensitivities of 1 -10 µBq/kg, and also allow to identify a break of secular equilibrium 10 in long-lived primordial decay chains. Once the more radio-pure materials are selected, their handling and cleaning must be thoroughly defined to limit the radiogenic contamination from cosmogenic activation that could occur during the transportation or the plating-out of radiogenic contaminants during their fabrications.

In addition to all the efforts done to select and handle radio-pure materials to build the detector, some experiments can use part of their detection medium as another layer of active shielding, as mentioned previously. This method requires the use of detection techniques allowing to reconstruct the position of interactions occurring in the sensitive detection medium. This method of self-shielding, so-called fiducialization, can further suppress the external background presented in the last two sections. One example of fiducialization was performed in the context of this study and will be presented in section 5.3.1.

Internal radiogenic backgrounds

The last category of background sources for rare-events searches experiments corresponds to the intrinsic contamination of the detection medium itself. Either naturally present in the detection medium, emanated from the air or materials, or produced through radiogenic or cosmogenic activation, internal radiogenic background sources cannot be shielded and are usually homogeneously distributed in the detection medium.

As a consequence, fiducialization will not be effective on this kind of backgrounds. Similarly to materials selection, special care for the procurement or production of a radio-pure detection medium as well as for its handling are required. For some detection medium, such as noble gases, purification prior to and during the operation time of the experiments is performed to further reduce its intrinsic contamination.

The Radon ( 222 Rn and 220 Rn) emanation (and its progenies) in the detection medium, is a problematic background common to most of the low-background experiments. As part of the 238 U primordial decay chain, radon accumulates in all the materials (as already discussed in the previous section) but is also present in the air 11 . The radon atoms can leave their creation site and emanate in the detection medium in two ways. The first option 9 Other techniques exist like α spectroscopy or neutron activation analysis, but were not used in this work. 10 The secular equilibrium in a decay chain is reached when the activities of all daughter nuclides are equal to the activities of their respective parents. A break of the secular equilibrium can occur when physical or chemical processes are applied to the raw material, impacting the specific activities of some nuclides in the decay chain.

11 Due to the emanation of radon from the rocks and soils all over the world. It implies that the detection medium must not be in direct contact with the ambient air. corresponds to radon nuclides on the surface of the material: they are ejected by the recoil induced by the α-decay of its mother nuclide ( 226 Ra and 224 Ra). The other option is driven by the diffusion of radon nuclides from deeper material layers and their subsequent emanation. Its presence emphasizes the necessity of using radiopure materials in contact with the detection medium. Strategies to mitigate radon emanation exist but depend on the detector technology employed. We can mention the coating of materials in contact with the detection medium. In some cases, e.g., liquid xenon target, emanated radon can be removed through dedicated purification systems such as cryogenics distillation column.

Depending on the technology used by low-background experiments different signatures originating by electronic or nuclear recoils interaction or even a discrimination between α, β, γ particles can be used to reject background events from both external and internal sources. The following section will propose an overview of the different observables that can be measured to detect rare events and their associated detector technologies.

Low background experiments

The interaction of a particle with the target medium of a low background experiment, can Germanium, silicium and directional detectors detectors for light and charge signals.

As mentioned in the previous section, one powerful tool that can be used by lowbackground experiments to mitigate the observed background rate in the detection medium is the discrimination power between different types of particles. The combination of two detection channels increases the discrimination power as it combines the response of the 12 Such as low-pressure gas detectors. 13 Such as bubble chambers or superheated fluids. 14 calorimetry through light and tracking of the energy deposition through charge measurements, a technology used in SuperNEMO [START_REF] Arnold | Probing new physics models of neutrinoless double beta decay with SuperNEMO[END_REF]. detection medium to interactions which is proportional to the deposited energy, with the relative contribution of the signal that also depends on the type of the interacting particle.

Other techniques of particle identification and discrimination exist, one of which is based on pulse shape analysis of the measured signals and depends on the detection medium. Among the different detector technologies mentioned above, the most commonly used for rare events search are illustrated in figure 1.7, and their main characteristics and advantages/inconveniences are presented in more detail in the following.

Arrays of high-purity scintillator crystals (see figure 1.7 a), such as DAMA [START_REF] Bernabei | First model independent results from DAMA/LIBRA-phase2[END_REF], COSINE-100 [START_REF] Adhikari | An experiment to search for dark-matter interactions using sodium iodide detectors[END_REF] or SABRE [START_REF] Antonello | The SABRE project and the SABRE proof-ofprinciple[END_REF], can achieve large target masses of O(100) kg. This technology of detector is mostly used for DM annual modulation search since the target crystals employed are mainly NaI(Tl), but also CsI(Tl), whose high mass numbers boost the sensitivity for DM interaction 15 . One of the main challenge of these detectors is the reduction of their rather large intrinsic backgrounds 16 . Another limit comes from the impossibility to employ fiducialistation and particle discrimination.

Germanium and silicon semiconductor ionisation detectors, such as CDEX-10 [START_REF] Jiang | Limits on light weakly interacting massive particles from the first 102.8 kg × day data of the CDEX-10 experiment[END_REF], GERDA [START_REF] Agostini | Upgrade for Phase II of the GERDA experiment[END_REF], or LEGEND [65], measure only the charge signal by collecting the electrons/holes pair created in the solid state detection medium. They exhibit an excellent energy resolution and low energy thresholds thanks to the low amount of energy needed to create an electron-hole pair (Ge: 2.9 eV, Si: 3.6 eV). However, their scalability is challenging due to high electronic noise that limits the mass of each crystal to the O(1) kg scale, 15 More precisely to spin-independent interactions, whose notion will be introduced in chapter 2. 16 lowest background level achieved is ∼ 1 events/kg/day/keV from [START_REF] Bernabei | First model independent results from DAMA/LIBRA-phase2[END_REF]. leading to a structure of crystals arrays. Silicon detectors can be used as charge-coupled devices (CCDs), as done in DAMIC [START_REF] Aguilar-Arevalo | Results on low-mass weakly interacting massive particles from an 11 kg x d target exposure of DAMIC at SNOLAB[END_REF], which has the advantage of track reconstruction for particle identification. In contrast, germanium detectors use pulse shape discrimination as a particle identification tool. They are less impacted by background from surface events due to the overall larger size of crystals with respect to silicium CCDs.

Experiments based on the detection of the heat necessarly use cryogenics, like crystalline cryogenic detectors (bolometers), which operate at low temperature (typically ≤ 50 mK) to minimize the heat capacity and the thermal fluctuation noise. They measure the heat signal through thermal or athermal phonons induced by the tiny temperature increase ∆T from the deposited energy. A thermal sensor, in contact with the crystal, allows to derive the heat increase from the induced resistivity variation. Cryogenic detectors feature a precise energy measurement with almost no quenching 17 in the heat 17 Loss of information on the true deposited energy due to dissipation through other signal channels not sensitive by the experiments. This effect is almost inexistent for detectors measuring the heat channel since ionization and scintillation will ultimately be converted to heat. channel, excellent energy resolution and background rejection through pulse shape discrimination is feasible. However, using only heat channels, particle identification, and track reconstruction is impossible. Furthermore, the operation at mK-temperatures over a long period is challenging and expensive, especially in the process of increasing the scale of experiments towards the ton scale. Experiments, based on low temperature bolometers technology, can use a wide variety of crystal materials like: CaWO 4 in CRESST [START_REF] Abdelhameed | First results from the CRESST-III low-mass dark matter program[END_REF], or Ge in RICOCHET [START_REF] Billard | Coherent neutrino scattering with low temperature bolometers at Chooz reactor complex[END_REF] and CUORE [START_REF] Adams | CUORE opens the door to tonne-scale cryogenics experiments[END_REF]. The possibility to use a second signal channel, like ionisation in semiconductors (Ge, Si), as done in EDELWEISS [START_REF] Armengaud | Performance of the EDELWEISS-III experiment for direct dark matter searches[END_REF] and SuperCDMS [START_REF] Agnese | Projected sensitivity of the SuperCDMS SNOLAB experiment[END_REF],

or scintillation in scintillating crystals, as in AMoRE [START_REF] Ejiri | A CaMoO 4 crystal low temperature detector for the AMoRE neutrinoless double beta decay search[END_REF], CUPID [START_REF]CUPID pre-CDR[END_REF], or COSINUS [START_REF] Angloher | The COSINUS project: perspectives of a NaI scintillating calorimeter for dark matter search[END_REF],

provide an additional information on the ionization and scintillation yields that allow interaction type identification. Figure 1.7 b, illustrates the working principle of cryogenic bolometers with charge readout.

Liquid scintillating detectors measuring only the scintillation signal usually use a spherical target surrounded by photomultipliers, as shown in figure 1.7 c, to optimize the light collection efficiency. This is a mature technology deployed in many experiments searching for rare events, such as KamLAND-Zen [START_REF] Abe | First Search for the Majorana Nature of Neutrinos in the Inverted Mass Ordering Region with KamLAND[END_REF], SNO+ [START_REF] Albanese | The SNO+ experiment[END_REF] and DEAP-3600 [START_REF] Ajaj | Search for dark matter with a 231-day exposure of liquid argon using DEAP-3600 at SNOLAB[END_REF].

These experiments already demonstrated their capacity to perform large exposure data taking at the tonne × year scale. Through the photon hit timing and the signal distribution, such detectors can reconstruct the interaction position allowing the fiducialization of the detection medium. Depending on the liquid scintillator employed, pulse shape discrimination can be used to make particle identification due to differences in scintillation One particular category of scintillator widely used nowadays in low-background experiments is noble gases such as Argon and Xenon. Their potential is fully exploited in detectors such as Time Projection Chambers (TPC), whose dual-phase liquid/gas configuration is illustrated in figure 1.7 d. This detector technology is sensitive to both primary scintillation signal and ionization electrons signals allowing for fiducialization via reconstruction of the interaction position and background discrimination using pulse shape discrimination or particle identification. Dual-phase noble gas TPCs are used in experiments such as DarkSide-50 [START_REF] Agnes | Low-mass dark matter search with the DarkSide-50 experiment[END_REF] (Ar-based) and XENONnT [START_REF] Aprile | Projected WIMP sensitivity of the XENONnT dark matter experiment[END_REF], this latter one will be presented in more detail in chapter 3. They benefit from the high shielding power of noble gases and also can achieve lower energy threshold of O(1) keV. Liquid single-phase TPCs are also used for rare event search, like in nEXO [START_REF] Adhikari | nEXO: neutrinoless double beta decay search beyond 10 28 year half-life sensitivity[END_REF].

In the family of metastables detectors, we can mention bubble chamber detectors such as PICO [START_REF] Amole | Dark matter search results from the PICO-2L c 3 f 8 bubble chamber[END_REF], that use superheated liquids 18 as target materials. Energy deposition above some threshold will lead to a local phase transition producing bubble whose number and position are recorded with stereoscopic camera readout, as shown in figure 1.7 e. One strength of this detection technology is its capacity to be only sensitive to a specific type of interaction, such as nuclear recoil, by fine-tuning the operational parameters that drive the bubble formation probability. However, such detectors suffer from complex operation conditions 19 and complicated detector calibration.

Gaseous time projection chamber detectors are able to reconstruct the track of the interaction using the information carried out by the ionization channel. Electrons released during the energy deposition are drifted by a homogeneous field to the readout plane. The particle identification can thus be made with this detection technology, in addition to the position reconstruction. Among the various target gas available, the most commonly used are CF4 and nobles gases like xenon. Gaseous TPC can be classified into two different categories. First, the low-pressure TPCs, as shown in figure 1.7 f, can act as directional experiments by looking at the topology of the tracks 20 . It is the technology used by the DRIFT experiment [START_REF] Battat | Low threshold results and limits from the DRIFT directional dark matter detector[END_REF] for example. The second category of gaseous TPCs aims to maximize their exposure using high-pressure vessels. In the case of noble gases target, the scintillation channel can also be used to provide additional information for background discrimination. However, gaseous TPCs don't have a self-shielding power as efficient as in liquid TPC. Thus reaching the same level of background can be challenging. 18 Kept at a temperature just above their boiling point. 19 The long time scales to establish the superheated state lead to significant dead times. 20 Longer tracks facilitate the reconstruction of the directionality since track length depends on the target density. The scalability of gaseous TPC might not be as strong as in liquid TPC, but projects such as the NEXT experiment [START_REF] Novella | Measurement of the 136 Xe two-neutrino double-β-decay half-life via direct background subtraction in NEXT[END_REF] aim to reach the multi-tonne × year scale of exposure.

Low-background experiments can exploit a large variety of background mitigation strategies and detection technology in order to look for rare events searches. Depending on the physical process of interest, one category of detectors will be more suitable than the others. Thus a more thorough comprehension of this process is necessary to understand the choice of detection technics. In the next chapter, we will introduce in more detail the two major rare processes of interest in this thesis, i.e., the direct detection of dark matter, which is the primary goal of the XENONnT experiment, and the search for 0νββ decay, which is the main subject of this thesis.

2

Chapter 2

Neutrino physics and Dark Matter direct detection

In the realm of rare processes which are of interest for particle physics, astrophysics and cosmology worldwide, two emblematic names come to mind directly: neutrino and Dark Matter. The neutrino is a fundamental particle of the Standard Model whose one of its characteristics is to very weakly interact with matter, making its study a challenging task. Our current understanding of this particle is introduced in section 2.1, along with the remaining unknowns, notably related to the origin of its mass, that will be discussed in section 2.1.2. The different types of neutrino interactions will be presented in section 2.1.1.

They are not the only way to shed light on the remaining dark spots of the neutrino sector.

One of the best probes to enlighten on its nature consists in the search for a rare nuclear process called neutrinoless double-β decay -the subject of this thesis -which is a particular double weak decay that could open a window to new physics and is further developed in section 2.1.3.

An other main priority of modern physics nowadays is the search for Dark Matter (DM), a weakly interacting, massive, and non-baryonic matter still undetected so far, that will be introduced in section 2.2. The concept of DM and the mains evidences that motivate its search are presented in section 2.2.1, while the plethora of theoretical DM particle candidates will be discussed in section 2.2.2, with a focus on the weakly interacting massive particles family whose observation is the main goal of the XENONnT experiment. The interaction of a DM candidate with a target in ground-based low-background experiments, will be described in section 2.2.3. This chapter will conclude in section 2.3 by highlighting the possibility of looking for both rare processes using the same XENONnT detector.

2

Chapter 2. Neutrino physics and Dark Matter direct detection

Introduction to neutrino physics and double weak decay

In the history of physics, several disagreements between experimental observations and theoretical predictions have been solved by assuming the existence of a new particle. As an example, after the discovery of the nuclear β-decay in 1899 by E. Rutherford and the measurement of a continuous energy spectrum by J. Chadwick in 1914, physicists were puzzled due to the apparent violation of the energy conservation law. Indeed, at that time the β --decay was seen as the decay of a parent nucleus X Z to a daughter nucleus X Z+1 with the emission of an electron: X Z → X Z+1 + e -. Therefore, the electron was expected to carry almost all the energy available in the reaction, leading to a discrete energy spectrum. Two hypothesis to explain the observation can be put in place: either the energy conservation law is wrong or incomplete, or a new particle that could explain the observation while preserving the theory was not considered. A solution came in 1930 from W. Pauli who proposed the existence of a third, weakly interacting and neutral particle emitted in the β decay, whose properties explain why it was not observed to date [START_REF] Pauli | Letter to the physical society of tubingen[END_REF].

This particle was named neutrino by E. Fermi in 1934, while he was develloping its theory of the β-decay. Following this, many experiments were built to detect neutrinos and confirm the proposed solution by Pauli. The discoveries of the electron neutrino1 in 1956 by F. Reines and C.L. Cowan [START_REF] Reines | The neutrino[END_REF], muon neutrino in 1961 by L.M. Lederman, M. Schwartz and J. Steinberger [START_REF] Danby | Observation of high-energy neutrino reactions and the existence of two kinds of neutrinos[END_REF], and tau neutrino in 2001 by the DONUT collaboration [START_REF] Kodama | Observation of tau neutrino interactions[END_REF] leads to the three flavors neutrino paradigm currently used in the Standard Model of particle physics.

The Standard Model (SM) [START_REF] Sheldon | Partial-symmetries of weak interactions[END_REF][START_REF] Weinberg | A model of leptons[END_REF][START_REF] Salam | Weak and electromagnetic interactions[END_REF] is so far the most successful model to describe the elementary particles properties and their interactions through three of the fundamental forces: the electromagnetic, strong and weak forces2 . In the SM, elementary particles are divided into fermions, which have non-integer 1/2 spin (and which could be further distinguished between lepton and quarks), and bosons, which have an integer spin, as summarized in figure 2.1. Fermions are the fundamental constituents of matter and are classified into three families (or generations). The six fermions coupled to the strong interaction are called quarks. They participate in all three interactions described in the SM. The six fermions that do not couple to the strong interactions are called leptons, among them we can differentiate the charged leptons (e -, µ -, τ -) that couple to both electromagnetic and weak interaction, and the neutral leptons, i.e., neutrinos, that also have three flavors linked to the charged lepton, (ν e , ν µ , ν τ ), and only couple to the weak interaction.

2

Introduction to neutrino physics and double weak decay

The mathematical representation of the SM is a gauge theory under the local symmetry group SU (3) C ⊗ SU (2) L ⊗ U (1) Y that describes the interactions and the gauge bosons as interaction carriers. The SU (3) C group describe the theory of strong interaction and concern particles with a charge of color C, i.e., quarks and gluons, where the latters are mediators of the strong interaction. The SU (2) L ⊗ U (1) Y group corresponds to the unification of the electromagnetic and weak interactions into the electroweak theory. Where L refers to left-handed fields 3 and Y the weak hypercharge 4 . The W ± and Z 0 bosons are the carriers of the weak interaction, while the photon is the carrier of the electromagnetic interaction. The last ingredient completing the SM is the Higgs scalar boson H, discovered in 2012 by the ATLAS and CMS experiments [START_REF] Aad | Observation of a new particle in the search for the standard model higgs boson with the ATLAS detector at the LHC[END_REF][START_REF] Chatrchyan | Observation of a new boson at a mass of 125 gev with the CMS experiment at the LHC[END_REF]. It is responsible for the generation of masses for weak bosons (W ± , Z 0 ) and fermions through the so-called Brout-Englert-Higgs mechanism [START_REF] Higgs | Broken symmetries and the masses of gauge bosons[END_REF][START_REF] Guralnik | Global conservation laws and massless particles[END_REF][START_REF] Englert | Broken symmetry and the mass of gauge vector mesons[END_REF] The break of parity symmetry 5 observed in the weak interection [START_REF] Wu | Experimental test of parity conservation in beta decay[END_REF], leads to a difference in the chirality 6 between left-(right-)chiral (anti-)fermion that couple to the weak interaction and the right-(left-)chiral (anti-)fermion that do not. In parallel, the helicity 7

3 Meaning that it affects only left-chiral fermions. 4 The weak hypercharge Y is linked to the charge Q of the particle and the third component of the weak isospin quantum number T 3 through the relation: Q = 1 2 Y + T 3 . 5 Equations of physics are invariant under mirror inversion. 6 Particle wave function transforms with a right-or left-handed representation of the Poincare group. 7 Helicity is a projection of the spin onto the direction of the momentum. Left-(right-)handed particles In addition to the neutrino-electron scattering, neutrinos can also scatter off the nucleus through the exchange of a Z 0 boson (NC). In the case of a low-energy neutrino (< O(100) MeV) the neutrino will interact coherently10 with the whole nucleus, while at higher energy, it will interact with the individual nucleons (or quarks). In 1974, Daniel Z. Freedman predicted the existence of an elastic scattering process that would benefit from a coherent enhancement proportional to the size of the nucleus, called coherent elastic neutrino-nucleus scattering [START_REF] Daniel | Coherent effects of a weak neutral current[END_REF]. So far, only the COHERENT experiment has claimed its detection [START_REF] Akimov | Observation of coherent elastic neutrino-nucleus scattering[END_REF], which is quite challenging due to the difficulty of observing the tiny nuclear recoil induced by the CEvNS. Unlike neutrino interactions with a single fermion that are very well known, the CEvNS interaction description is much more complicated due to the complex structure of the nucleus. The differential cross section as a function of the nuclear recoil energy (T r ) and neutrino energy (E ν ) is given by [START_REF] Dutta | Neutrino physics with dark matter detectors[END_REF]:

dσ (E ν , T r ) dT r = G 2 F π m N (Zg p v + N g n v ) 2 1 - m N T r 2E 2 ν F 2 (T r ) (2.2)
where m N is the target nucleus mass, N the number of neutrons, Z the number of neutrons,

g n v = -1/2, g p v = 1/2 -2 sin 2 θ w ,
and F (T r ) is the nuclear form factor which describes the loss of coherence due to the internal structure of the nucleus, whose typical parametrisation is the Helm form factor [START_REF] Lewin | Review of mathematics, numerical factors, and corrections for dark matter experiments based on elastic nuclear recoil[END_REF]. When the wavelength of the scattering is longer than the size of the nucleus, F (T r ) → 1. This condition is satisfied for nearly all nuclear targets when neutrino energies are below 10 MeV, enhancing the CEvNS interaction cross-section with the nucleus that grows as the square of the number of neutrons, N 2 . The signature of such interaction being a low energy nuclear recoil, it is a natural background source for the search of DM direct detection, which will be introduced in section 2.2.3. However, it would also confirm the previous observation from COHERENT of such a rare process whose experimental study is still recent.

Neutrino Mass and Oscillation

As described in the previous sections, it is possible to describe the weak interaction of neutrinos with the matter via the exchange of neutral and charge currents: it is thus possible to build experiments aiming at detecting such interactions. This section will detail the discovery of the neutrino mass and the neutrino flavor oscillation mechanism behind it (that might indicates the presence of physics beyond the SM).

2

2.1. Introduction to neutrino physics and double weak decay

Discovery of the neutrino mass

The first hint for neutrino oscillation comes from the observed deficit, with respect to the prediction, of the electron neutrino flux from the sun, measured by R. Davis and J.

Bahcall [START_REF] Bahcall | Solar neutrinos: A scientific puzzle[END_REF]. This deficit was then confirmed by other experiments [START_REF] Cribier | Results of the whole GALLEX experiment[END_REF][START_REF] Abdurashitov | Solar neutrino flux measurements by the soviet-american gallium experiment (sage) for half the 22-year solar cycle[END_REF][START_REF] Hirata | Observation of 8 B solar neutrinos in the Kamiokande-II detector[END_REF]. If the flavor of the neutrino can change, this could explain those observations. The first proposition of neutrino oscillation was initially proposed by B. Pontecorvo for ν → ν [START_REF] Pontecorvo | Inverse beta processes and nonconservation of lepton charge[END_REF], then Maki, Nagava, and Sakata proposed a different form of oscillation related to the neutrino flavor ν e → ν µ [START_REF] Maki | Remarks on the unified model of elementary particles[END_REF]. The experimental confirmation of neutrino flavor oscillation was detected for the first time in 1998 by Super-Kamiokande [START_REF] Fukuda | Evidence for oscillation of atmospheric neutrinos[END_REF] for atmospheric neutrino, and later on by SNO [START_REF] Ahmad | Direct evidence for neutrino flavor transformation from neutral-current interactions in the Sudbury Neutrino Observatory[END_REF] in 2002 for solar neutrino and KamLAND [START_REF] Araki | Measurement of neutrino oscillation with KamLAND: Evidence of spectral distortion[END_REF] in 2004 for reactor neutrino.

In the three flavor neutrino oscillation framework, assuming a non-zero mass for the neutrino, it is possible to define the flavor eigenstates |ν α ⟩, with α = (e, µ, τ), as combination of the mass eigenstates |ν i ⟩, with i = (1, 2, 3), whose mixture is given by:

|ν α ⟩ = 3 i=1 U αi |ν i ⟩ (2.3)
where the coefficients U αi are elements of 3×3 the Pontecorvo-Maki-Nakagawa-Sakata (PMNS) neutrino unitary mixing matrix:

     ν e ν µ ν τ      =      U e1 U e2 U e3 U µ1 U µ2 U µ3 U τ1 U τ2 U τ3      ×      ν 1 ν 2 ν 3      (2.4)
The PMNS matrix is commonly parameterized by three mixing angles (θ 12 , θ 23 , and θ 13 ), a CP (charge parity symmetry) violation phase δ CP , and α 1,2 additional CP violation phases needed if the neutrino is a Majorana particle11 but does not impact the probability of oscillation and thus will be omitted in the following. The matrix in equation 2.4 can be written as:

U PMNS =      1 0 0 0 c 23 s 23 0 -s 23 c 23      ×      c 13 0 s 13 e -iδ CP 0 1 0 -s 13 e iδ CP 0 c 13      ×      c 12 s 12 0 -s 12 c 12 0 0 0 1      ×      1 0 0 0 e iα 1 0 0 0 e iα 2      (2.5) with c ij = cos(θ ij ), s ij = sin(θ ij ).
It follows that the time evolution of a propagating 2 2

Chapter 2. Neutrino physics and Dark Matter direct detection neutrino initially in a mass eigenstates |ν i (0)⟩ is given by:

|ν i (t)⟩ = e -i(E i t-p i L) |ν i (0)⟩ (2.6)
where E i , p i are respectively the energy and momentum of the neutrino, and L the traveled distance. Assuming an ultra-relativistic neutrino, p i ≫ m i , we can use the approximation:

E i = p 2 i + m 2 i ≃ p i + m 2 i 2p i ≃ p i + m 2 i 2E i (2.7)
to express the time evolution as:

|ν i (t)⟩ = e -i m 2 i 2E i L |ν i (0)⟩ (2.8)
The evolution of the flavor eigenstates of the neutrino can then be expressed, from equation 2.3 using equation 2.8, as following:

|ν α (t)⟩ = i U αi e -i m 2 i 2E i L |ν i (0)⟩ = i U αi e -i m 2 i 2E i L γ U * γi |ν γ (0)⟩ = γ i U * γi e -i m 2 i 2E i L U αi |ν γ (0)⟩ (2.9)
Finally, the probability to detect a neutrino in the flavor α after traveling a distance L, knowing that it was produced in the flavor β with an energy E, is given by:

P (ν β → ν α ) = |⟨ν α (t) | ν β (0)⟩| 2 = γ i U * αi e i m 2 i 2E L U γi ⟨ν γ (0) | ν β (0)⟩ 2 = i U βi e i m 2 i 2E L U * αi 2 = i,j U αi U * βi U * αj U βj e -i( ∆m 2 ij 2E )L (2.10)
with ∆m 2 i,j = m 2 i -m 2 j the difference of the square of the masses relative to the ν i and ν j eigenstates. From equation 2.10 it follows that if the neutrinos are massless, then ∆m i,j is null and the flavor oscillation of neutrino is not possible. Therefore the observation of neutrino flavor oscillation demonstrates that neutrinos are massive particles.

Measure of oscillation parameters and neutrino mass

Many experiments aim to study the neutrino oscillations phenomenon by measuring the different parameters of the PMNS matrix with the highest precision. The three mixing angles (θ 12 , θ 23 , and θ 13 ), the CP violation (δ CP ) and mass (∆m 2 i,j ) terms are the major 2 2

2.1. Introduction to neutrino physics and double weak decay goals of the current and future neutrino experiments. Nevertheless, experiments studying neutrino flavor oscillation can only constraints the ∆m 2 i,j terms through measurement of the phase (ϕ ij ) of equation 2.10 that can be written as:

ϕ ij = 1.27∆m 2 ij eV 2 L[km] E[GeV] (2.11)
where the 1.27 factor comes from reintroducing the values of c and ℏ such that L is expressed in km and E in GeV.

Oscillation experiments can be grouped into four different typologies; each one focused on studying one specific source of neutrino covering a different range of L/E and thus studying oscillations between different flavors i, j.

• Solar neutrinos experiments: Using the Sun as a source of electron neutrinos 12 , experiments, such as Borexino [START_REF] Agostini | Experimental evidence of neutrinos produced in the CNO fusion cycle in the sun[END_REF], and Super-Kamiokande [START_REF] Abe | Solar neutrino results in Super-Kamiokande-III[END_REF], can constraints precisely the θ 12 angle and measure ∆m 2 12 and θ 13 . This source of neutrino corresponds to a distance L ∼ 10 11 m and neutrino energy E ≤ 15 MeV.

• Atmospheric and cosmogenic neutrinos experiments:

The Super-Kamiokande [START_REF] Abe | Atmospheric neutrino oscillation analysis with external constraints in Super-Kamiokande I-IV[END_REF] and IceCube [START_REF] Aartsen | Determining neutrino oscillation parameters from atmospheric muon neutrino disappearance with three years of IceCube DeepCore data[END_REF] experiments study neutrinos produced in extensive air shower from cosmic air, that corresponds to a source of neutrino from 20 < L < 10 3

km with an energy E ∼ 1 GeV, but also high energy neutrinos (E ≥ 1 PeV) from cosmogenic sources. Those experiments can probe θ 23 , θ 13 , ∆m 2 32 and δ CP parameters, but suffer from a lower precision compare to the others category of experiments.

• Accelerator neutrinos experiments: Also called long baseline neutrino beam

experiments, this category of experiment study the oscillation of a ν µ /ν µ beam produced by a particle accelerator 13 . The distance between the source and the detector is in the range L ≳ 500 km with a neutrino beam energy of E ≃ 1 GeV. The current best results on the measurements on θ 23 , |∆m 2 23 |, and δ CP comes from the T2K [START_REF] Abe | Constraint on the matter-antimatter symmetry-violating phase in neutrino oscillations[END_REF] and NOvA [START_REF] Acero | Improved measurement of neutrino oscillation parameters by the NOvA experiment[END_REF] experiments. They are also sensitive to the θ 13 parameter.

• Reactor neutrinos experiments: Nuclear reactors are powerful sources of νe with an energy E ≃ 3 MeV that are produced from the numerous β-decay occurring in the core of the reactor. It corresponds to a source of neutrinos with a rather "short" distance to the detector (L ≃ 10 -10 4 m) with respect to the other categories. We can mention Double Chooz [START_REF] De Kerret | Double Chooz θ 13 measurement via total neutron capture detection[END_REF], Daya-Bay [START_REF] Adey | Measurement of the electron antineutrino oscillation with 1958 days of operation at Daya Bay[END_REF], and RENO [START_REF] Shin | Observation of reactor antineutrino disappearance using delayed neutron capture on hydrogen at RENO[END_REF] 2 2

Chapter 2. Neutrino physics and Dark Matter direct detection among the major experiments focusing on the measurements of θ 13 , |∆m 2 23 |, but also KamLAND [START_REF] Eguchi | First results from KamLAND: Evidence for reactor antineutrino disappearance[END_REF] for θ 12 , ∆m 2 21 parameters.

From the current best results on neutrino oscillation parameter [START_REF] Ivan Esteban | The fate of hints: updated global analysis of three-flavor neutrino oscillations[END_REF], we know that Direct measurement: Precise measurement of the β-decay energy spectrum allows to perform a direct measurement of the neutrino mass. Indeed, in this process, the available energy Q β is shared between the emitted electron and electron anti-neutrino, leading to a continuous energy spectrum for the β particle. The end-point of the spectrum corresponds to the scenario where the kinematic energy of the neutrino is null. Thus the maximal energy possible for the electron is Q β -m ν c 2 , as illustrated in figure 2.5 for a tritium isotope used by the KATRIN [START_REF]KATRIN: A next generation tritium beta decay experiment with sub-ev sensitivity for the electron neutrino mass[END_REF] experiment. One advantage of this direct measurement is that it does not rely on an underlying theory and thus is model-independent.

The current best constraints come from the KATRIN experiment that set an upper limit on the absolute mass of the neutrino with a 90% confidence level of [START_REF] Aker | Direct neutrino-mass measurement with sub-electronvolt sensitivity[END_REF]:

m β = 3 i=1 |U ei | 2 m 2 i < 0.8 eV (2.12)
Indirect measurements: Contrary to the model-independent direct measurements, two other options that rely on the validity of underlying models can constrain the neutrino mass:

• Analysis of anisotropies in the Cosmic Microwave Background (CMB) (see section 2.2.1), the first picture of the universe after the decoupling of photons with the matter, in the context of the standard model of cosmology (Λ -CDM ), allow to constrain the sum of the neutrino mass eigenstates m Σ . The latest results based on measurements from the Planck collaboration [START_REF] Aghanim | results[END_REF] give an upper limit with a 95% confidence level of [START_REF] Shouvik | Updated results on neutrino mass and mass hierarchy from cosmology with Planck 2018 likelihoods[END_REF]:

m Σ = i m i <      0.15 eV (NO) 0.17 eV (IO) (2.13)
• If the neutrino is a Majorana particle, the observation of a 0νββ decay, in the context of the light Majorana neutrino exchange mechanism, could allow to derive its effective mass m ββ . This approach is studied in this thesis and will be further detailed in section 2.1.3.2.

Origin of the neutrino mass

Despite the historical hypothesis of neutrinos as massless particles, introduced at the beginning of section 2.1, the observation of the neutrino flavor oscillation phenomenon, presented in section 2.1.2, is an undeniable evidence of the very small (< 1 eV) but nonnull neutrino mass. To reconcile the presence of the neutrino mass within the SM it is necessary to define the mechanisms responsible for it. The three major mechanisms considered nowadays are presented in the following.

Dirac mass term:

In this hypothesis, neutrinos are considered to be massive Dirac fermions like the other fermions (e ± , µ ± , τ ± ), with a mass at rest m. Thus, they are described as a Dirac spinor ψ, solution of the Dirac equation:

(iγ µ ∂ µ -m) ψ = 0 (2.14)
Where ∂ µ is the covariant derivative, and γ µ are the Dirac matrices:

γ 0 =   I 0 0 -I   and γ i =   0 σ i -σ i 0   (2.15)
with I the (2 × 2) identitiy matrix and σ i the Pauli matrices:

σ 1 =   0 1 1 0   , σ 2 =   0 -i i 0   and σ 3 =   1 0 0 -1   (2.16)
Knowing that two chirality states left-(L) and right-(R) handed, are possible in the case of massive fermions, it is possible to extract the two components ψ L and ψ R using the P L , P R projectors and taking into account that P L P R ψ = 0 from the Dirac matrices commutation, it follows:

ψ L = P L ψ = 1 2 (1 -γ 5 ) ψ ψ R = P R ψ = 1 2 (1 + γ 5 ) ψ (2.17)
Where γ 5 is the Dirac matrix defined as γ 5 = iγ 0 γ 1 γ 2 γ 3 which gives:

γ 5 =   0 I I 0   (2.18)
Neutrino masses can then be generated by the standard Higgs mechanism via the Yukawa interaction whose Lagrangian can be re-written, after the spontaneous breaking of the electroweak symmetry, in the following expression involving the Dirac mass term m D [START_REF] Bilenky | Neutrinoless double-beta decay: A probe of physics beyond the standard model[END_REF]:

2 2
2.1. Introduction to neutrino physics and double weak decay

-L D mass = ψm D ψ = m D (ψ L + ψ R ) (ψ L + ψ R ) = m D ψR ψ L + ψL ψ R (2.19)
This hypothesis requires the existence of a (left-)right-handed (anti-)neutrino to explain the existence of the neutrino mass, but so far, only (right-)left-handed (anti-)neutrinos have been observed. If neutrinos obtain their mass through the same mechanisms that the other fermions, this implies the existence of a (left-)right-handed (anti-)neutrino that does not couple to the weak interaction and only interacts through the gravitational force, the so called sterile neutrino. Furthermore, the difference in masses between neutrinos and the others fermions is rather large, more than six orders of magnitude, whose reason is quite hard to understand.

Majorana mass term: An alternative to the Dirac neutrino formalism was proposed by E. Majorana in 1937 with the initial assumption that neutrinos are their own antiparticles [START_REF] Majorana | Teoria simmetrica dell'elettrone e del positrone[END_REF]. It is possible to write the right-handed neutrinos as a parametrization of the left-handed ones. Using the charge conjugation matrix C, which satisfies the conditions:

Cγ T α C -1 = -γ α and C T = -C (2.20)
with γ α the Dirac matrices, and α = (0,...,3). Once applied to the L and R neutrinos (and similarly to the anti-neutrinos), it comes:

Cψ L → (ψ L ) c = (ψ c ) R and Cψ R → (ψ R ) c = (ψ c ) L (2.21)
The Majorana neutrino field ψ M , can then be expressed as:

ψ M = ψ L/R + ψ L/R c (2.22)
It is a solution of the Dirac equation, and two new independent mass terms, m L , and m R , are generated. It follows the Majorana mass term that can be expressed as:

L mass M = -ψM m L/R ψ M = -m L/R ψ L/R + ψ L/R c ψ L/R + ψ L/R c = -m L/R ψ L/R c ψ L/R + ψ L/R ψ L/R c = -m L/R ψ L/R c ψ L/R + m L/R ψ L/R ψ L/R c (2.23)
Thanks to the Majorana mechanism, it is possible to generate the neutrino mass without involving the weak Yukawa coupling to the Higgs fields mentioned in the Dirac

2

Chapter 2. Neutrino physics and Dark Matter direct detection mechanism. Still, it implements physics beyond the SM (BSM) since it broke the global U (1) symmetry responsible for the leptonic number conservation. Therefore, the Majorana nature of the neutrino allows processes where the leptonic number is not conserved (lepton number violating, LNV, processes), such as the 0νββ decay.

If the neutrino were found to be a Majorana particle, it will be the first Majorana particle found to exist. In addition, LNV processes could explain why matter dominates over anti-matter in our universe. This motivates the high interest in searching for such processes, as it will be further discussed in section 2.1.3.

Mixing Dirac and Majorana terms:

The last and most popular approach, also called the see-saw mechanism, allows to generate the neutrino mass and explains why it is so small with respect to the other fermions. It takes into account both Dirac and Majorana mass terms, assuming that neutrinos are Majorana particles again, and leads to the following general Lagrangian:

-L mass D+M = m D ψR ψ L + 1 2 m L (ψ L ) c ψ L + m R (ψ R ) c ψ R + m D ψL ψ R + 1 2 m L ψ L (ψ L ) c + m R ψ R (ψ R ) c (2.24)
Where the term 1 2 is a normalization factor to account for the non-independence of ψ L/R C and ψ L/R in equation 2.23. We can express the general Lagrangian in the matrix form, using two new fields that can be defined as spinors:

Ψ L =   ψ L ψ c L   =   ψ L (ψ R ) c   and Ψ R =   ψ c R ψ R   =   (ψ L ) c ψ R   (2.25)
This leads to the general mass term:

-L D+M masse = 1 2 ψ L (ψ R ) c   m L m D m D m R     (ψ L ) c ψ R   + h.c. = 1 2 ΨL   m L m D m D m R   Ψ R + h.c. ( 2

.26)

Where h.c. is the hermitian conjugate. The symmetric Majorana and Dirac masses matrix can be diagonalized in order to express the neutrino mass eigenstates m + and m - as:

m ± = ± 1 2 m L + m R ± (m L -m R ) 2 + 4m 2 D (2.27)
Considering m L = 0 to preserve the gauge symmetry and m D ≫ m R from the observed absence of interaction from right-handed neutrino, the two mass terms can be simplified as:

2

2.1. Introduction to neutrino physics and double weak decay

m + ∼ m R et m -∼ m 2 D m R (2.28)
And the two eigenstates become:

Ψ + = (ψ R + ψ c R ) + m D m R (ψ L + ψ c L ) Ψ -= (ψ L + ψ c L ) - m D m R (ψ R + ψ c R ) (2.

Double weak decays

Double weak decays are second-order processes in the SM of electroweak interactions.

They correspond to rare nuclear isobaric transitions from a parent double-even nucleus (A, Z) to a daughter nucleus (A, Z ± 2) by the simultaneous conversion of two nucleons.

This decay occurs if the parent nucleus (A, Z) has a lower mass and higher binding energy than the (A, Z ± 1) one and higher mass and lower binding energy than the (A, Z ± 2).

Thus no energetically favorable states are reachable by single-β decay. It is illustrated in figure 2.6, which shows the mass parabolas for nuclear isobars with even A derived from the semi-empirical Bethe-Weizsäcker mass formula based on the liquid drop nuclear model [START_REF] Saakyan | Two-neutrino double-beta decay[END_REF]:

M (A, Z) = Zm p + N m n -a V A + a S A 2/3 + a C Z 2 A 1/3 + a A (N -Z) 2 A + δ(A, Z) (2.30)
where Zm p and N m n are respectively the mass of all protons and of all neutrons in the nucleus. While the remaining terms represents the binding energy that holds the nucleus together 15 , with δ(A, Z) the pairing energy term that drives the probability for the nucleus 2 2

Chapter 2. Neutrino physics and Dark Matter direct detection

In the case of the neutrinoless mode, the 0νββ decay results in the conversion of two neutrons into two protons with the emission of two electrons, 2n → 2p + 2e -, and imply a clear violation of the leptonic number by two units, evidence of the BSM nature of this process and its underlying mechanism. A general expression for the half-life T 0ν 1/2 of this process takes the form [START_REF] Bilenky | Neutrinoless double-beta decay: A probe of physics beyond the standard model[END_REF]:

1 T 0ν 1/2 = G 0ν (g A ) 4 M 0ν 2 |f (m i , U ei )| 2 (2.36)
where G 0ν , and M 0ν are the neutrinoless version of the PSF and NME, respectively.

The term f (m i , U ei ) corresponds to an adimensional function containing the BSM physics that drives the decay. Among the numerous theoretical mechanisms developed to describe the 0νββ decay18 , we will focus on the most popular one, the light neutrino exchange mechanism, whose Feynman diagram is shown in figure 2.11. This mechanism implies a right helicity Majorana neutrino emitted from a W -boson and absorbed by another as a left helicity Majorana neutrino. It is possible only if the lepton number is violated and the exchanged neutrino is a massive Majorana particle, allowing the helicity flip. In this case, the BSM physics term of equation 2.36 can be expressed as [START_REF] Bilenky | Neutrinoless double-beta decay: A probe of physics beyond the standard model[END_REF]:

f (m i , U ei ) ≡ ⟨m ββ ⟩ m e = 1 m e i=1,2,3 U 2 ei m i (2.
⟨m ββ ⟩ = m 1 c 2 12 c 2 13 + m 2 s 2 12 c 2 13 e 2iα 1 + m 3 s 2 13 e 2iα 2 (2.38)
From this equation, it is clear that the determination of m ββ is not a direct measurement of the neutrino masses m i , since it also involves the mixing angles (θ 12 , θ 13 ), the As discussed in the introduction of the section 2.1.3, double-β decay can only occur in even-even nuclei whose single-β decay is forbidden. Among the various candidate isotopes, only a few of them have been or are actively studied to search for 0νββ decay. Indeed the choice of the studied isotopes is the first important step toward building an experiment.

One criterion is connected to the Q ββ of the isotope, which should be selected to be in a ROI with as less as possible background contamination, usually above 2 MeV. The second criterion is the target mass scalability of a given isotope, usually defined by its natural isotopic abundance or feasibility of target enrichment. In the following we will focus in the most studied isotopes nowadays, i.e. 76 Ge, 82 Se, 100 Mo, 130 Te, and 136 Xe. TPCs also has a leading role in the search for direct detection of Dark Matter, the second rare-event physics channel of interest in this thesis that will be introduced in the next section. This will serve as an introduction to better put the two subjects into the context of my work discussed in chapter 4 and chapter 5.

2

Chapter 2. Neutrino physics and Dark Matter direct detection

Dark Matter

The genesis of the concept of Dark Matter (DM), as it is considered nowadays, began in the early 20th century through multiple astronomical observations 20 , supporting the existence of an unknown component in our Universe. The well-known work from F. Zwicky in 1933 can be considered the starting point for a DM hypothesis. He observed the galaxies in the Coma cluster, whose velocity dispersion could not be explained taking only into account the gravitational interactions of visible matter under the assumption of the Virial theorem [START_REF] Zwicky | Die Rotverschiebung von extragalaktischen Nebeln[END_REF]. This observation can be explained if the existence of a uniformlydistributed halo of non-luminous and massive matter, named Dark Matter, encompassing galaxies is assumed. Since then, a multitude of astronomical and cosmological evidence accumulated on scales ranging from galaxies to the entire Universe, strengthening the motivation for the existence of DM and revealed its properties, as will be discussed in section 2.2.1. The nature itself of DM remains unknown, and a plethora of theoretical particle candidates emerged, as introduced in section 2.2.2. However, no direct observation of DM that would confirm its existence was achieved so far despite the tremendous experimental efforts ongoing (the XENON experiments played and are playing a leading role in this context), which is further presented in section 2.2.3.

2

2.2. Dark Matter

Dark Matter evidences

Almost forty years after F. Zwicky evidence of DM existence that did not convince the scientific community at that time, a new observation, this time at the galactic scale, came in 1978 from V. C. Rubin et al. that were studying the rotation curves of spiral galaxies in gravitational equilibrium [START_REF] Rubin | Extended rotation curves of high-luminosity spiral galaxies. IV. Systematic dynamical properties[END_REF]. They observed a star's velocities distribution close to flat at large radii to the center of the galaxy, rather than a Keplerian (r -1/2 ) decline as expected following Newtonian dynamics from the apparent luminous matter components. Once again, this phenomenon can be explained by assuming that most galaxies must contain more Dark Matter than visible matter in the form of a uniformly distributed halo. This evidence brought the DM hypothesis under the spotlight and has not faded away since then. An alternative solution to explain the behavior observed in the galaxy rotation curves is to assume that the law of gravitation is incomplete and that by modifying the theory, observation and prediction can be reconciled.

This approach led to the development of the Modified Newtonian Dynamics (MOND) [START_REF] Milgrom | A modification of the Newtonian dynamics as a possible alternative to the hidden mass hypothesis[END_REF].

However, the extended gravitation theories fail to explain all the different evidence of DM at different scales of the Universe.

Fig. 2.14 -Colourisation of Magellan images of the merging cluster 1E0657-558 (Bullet cluster), with overlay of mass distributions derived from X-ray spectroscopy made by the Chandra observatory [START_REF]NASA finds direct proof of dark matter[END_REF] in red, and from the gravitational lensing measurements [START_REF] Clowe | A direct empirical proof of the existence of dark matter[END_REF] in blue. Figure from [START_REF] Clowe | A direct empirical proof of the existence of dark matter[END_REF][START_REF]NASA finds direct proof of dark matter[END_REF].

The study of galaxy cluster collision is one of the most visual DM evidence that cannot be explained with modified gravitation theories. The comparison of mass distributions derived from X-ray emission measurements 21 (visible matter) and from gravitational 2 2

Chapter 2. Neutrino physics and Dark Matter direct detection lensing 22 (non-luminous and luminous matter) after the collision shows an apparent discrepancy. As shown in figure 2.14 for the merging cluster 1E0657-558, the reconstructed gravitational center from the total mass distribution (blue) is distinct from the visible matter one (red). Furthermore, the visible matter distribution exhibits a pattern characteristic of the interaction between the ordinary matter of the two clusters resulting in a bullet shape that gives the name of this particular cluster collision: The Bullet cluster.

This pattern is not visible in the total mass distribution, which can be interpreted as being due to DM haloes that continue their trajectories independently of the collision. This would represent a dominant component of the total mass budget. It also implies that DM is weakly interacting with the ordinary matter but also with itself [START_REF] Massey | The dark matter of gravitational lensing[END_REF]. Further evidences for DM also arise at the cosmological scale from the structure of the Universe [START_REF] Percival | The 2dF Galaxy Redshift Survey: the power spectrum and the matter content of the Universe[END_REF][START_REF] Daniel | Detection of the baryon acoustic peak in the large-scale correlation function of SDSS luminous red galaxies[END_REF] and the study of anisotropies in the cosmic microwave background (CMB) [START_REF] Aghanim | results[END_REF]. The CMB is the first picture of the Universe during its evolution, and corresponds to the times when photons decoupled from the electron-proton plasma, about 380 000 years after the Big Bang. The latest measurements of its residual radiation spectrum, corresponding to a black body emission with a temperature of 2.725 K, tectable X-rays. 22 The distortion of space-time caused by a gravitational potential (a large amount of mass from luminous and dark matter, acting as a lens), between a distant object and the observer, results in a deformation of the image of the distant object. The intensity of the image deformation can be used to infer the mass of the gravitational lens [START_REF] Refregier | Weak gravitational lensing by large-scale structure[END_REF].

2

2.2. Dark Matter from the Planck satellite [START_REF] Ade | Planck 2013 results. I. overview of products and scientific results[END_REF] have shown fluctuations at the 10 -5 -level. These fluctuations originate from matter density inhomogeneities and can be represented as an angular power spectrum as shown in figure 2.15. The CMB power spectrum can be described by the six-parameter standard model of cosmology, ΛCDM (Λ cold dark matter 23 ), which depends, among other parameters, to the baryonic matter, dark matter, and dark energy contents of the Universe. The ΛCDM model assumes the existence of cold DM (nonrelativistic DM particles), necessary to explain the current distribution of large-scale structure observed in the Universe [START_REF] Volker | The large-scale structure of the universe[END_REF]. Model predictions fits nicely the observed data (dashed black lines in figure 2.15) and allow to extract the relative contributions of dark energy (Ω Λ ), DM (Ω CDM ), and baryonic matter (Ω baryon ). The current best fit of the ΛCDM model to Planck data gives: [START_REF] Antonello | The SABRE project and the SABRE proof-ofprinciple[END_REF] Ω CDM = 0.2589 [START_REF] Salam | Weak and electromagnetic interactions[END_REF] Ω baryon = 0.0486 [START_REF] Domin | Neutrino accompanied β ± β ± , β + /ec and ec/ec processes within single state dominance hypothesis[END_REF] (2.41)

Ω Λ = 0.6911
From the various measurements and observations at different scales of the Universe, it is possible to infer several properties of a DM candidate that will be listed in the following.

• It must be massive since all the evidences of its existence are related to the gravitational interaction.

• It must be a non-baryonic matter that represent ∼ 25% of the total energymatter density in the Universe with a particle-like nature to explain the observed CMB anysotropies, and form haloes surrounding the existing baryonic structure (galaxies and clusters) to explain the rotation curves behavior at large radii of spiral galaxies.

• It must be stable or extremely long-lived since it is still present nowadays.

• It must be non-relativistic in order to explain the current structure of the Universe.

• It must not couple to the electromagnetic (neutral) and strong interactions otherwise it would have been already detected considereing its abundance.

• It must weakly interact with baryonic matter and itself in order to explain the mass distributions observed in galaxy cluster collisions.

WIMPs -Dark Matter candidates

If the particle nature of DM is assumed, its direct observation will be an evidence for physics beyond the standard model. A plethora of theoretical DM particle candidates, fulfilling the properties listed previously, were suggested in order to solve the DM co-

2

Chapter 2. Neutrino physics and Dark Matter direct detection nundrum. It leads to a broad landscape of DM candidates, whose masses range nearly over 50 orders of magnitude from 10 -21 eV (fuzzy DM) up to 10 18 GeV (primordial black hole) [START_REF] Billard | Direct detection of dark matter-APPEC committee report[END_REF]. One of the most appealing DM candidates over the last few decades are Weakly Interacting Massive Particles (WIMPs), which arises from BSM theory such as supersymmetry [START_REF] Jungman | Supersymmetric dark matter[END_REF], among other extensions of the SM [START_REF] Bertone | Particle dark matter: evidence, candidates and constraints[END_REF]. The WIMP's popularity comes from the fact that it can naturally explain the current dark matter density if the WIMP annihilation cross section is of the order of the weak scale. This is commonly regarded as the WIMP miracle.

Thermal production is the standard generation mechanism of WIMPs considered. It involves the production of WIMPs through the collision between SM particles during the very early and hot stage of the Universe (radiation era). At the same time, SM particles can be produced through WIMP annihilation, leading to a thermal equilibrium regime whose interaction rate is given by:

Γ A = n eq χ ⟨σ A v⟩ (2.42)
where n eq χ is the WIMP density at the time of the equilibrium, σ A is the annihilation cross-section, and v is the WIMP velocity. While the Universe expands, it cools down, reaching a temperature below the WIMP mass m χ leading to a break of the thermal equilibrium. From that moment, the WIMP density (n χ ) dropped according to the Boltzmann equation [START_REF] Workman | Review of Particle Physics[END_REF]:

dn χ dt -3Hn χ = -⟨σ A v⟩ n 2 χ -(n eq χ ) 2 (2.43)
where H is the Hubble constant [START_REF] Aghanim | results[END_REF]. From equation 2.43 we see that when WIMPs production and annihilation are in equilibrium, the WIMP density decrease due to the Universe's expansion. When the interaction rate becomes smaller than the Universe's expansion rate, both annihilation and production processes stop, causing the WIMPs co-moving density to freeze-out, as illustrated in figure 2. [START_REF] Dolinski | Neutrinoless double-beta decay: Status and prospects[END_REF]. The resulting WIMP thermal relic density is still observable today and depends on the annihilation cross-section. Considering a annihilation cross-section at the weak interaction scale (σ A = σ EW ≈ 10 -8 GeV -2 ), it leads to a relic density Ω χ ≈ 0.25, which is very close to the measured value Ω CDM = 0.2589 [START_REF] Salam | Weak and electromagnetic interactions[END_REF] (discussed in the previous section): the so called WIMP miracle. The typical prediction for WIMPs masses range from 1 to 10 5 GeV [START_REF] Roszkowski | Particle dark matter -a theorist's perspective[END_REF].

The WIMP search motivated the development of many experiments, including XENONnT discussed in this thesis. Therefore, while many alternative dark matter candidates exist, such as heavy right-handed neutrinos [START_REF] Shaposhnikov | The νMSM, inflation, and dark matter[END_REF] and axions or axions-like particles (ALPs) [START_REF] Ringwald | Exploring the role of axions and other WISPs in the dark universe[END_REF],

we will not develop them any further and will only focus on the WIMP detection principle in the following. [START_REF] Guido | Dark matter astrophysics[END_REF][START_REF] Kolb | The Early Universe[END_REF]. The x-axis (m/T) is the ratio between the WIMP mass, m, and the temperature, T , and it is proportional to the time starting from the Big Bang.

Dark Matter direct detection

Three approaches used to search for observe WIMPs other than by its gravitational interaction: its production through SM particles collision at colliders, indirect search for WIMP pair annihilation signature from astrophysical objects, and direct search of WIMP scattering off SM particles in ground-based experiments. Those three different detection channels are illustrated in figure 2.17. The indirect search and production at colliders approach will only be the object of an introduction in this section. While the direct detection approach, which is the method used by the XENON experiments, will be discussed in more details, along with a summary of the current state of the art of WIMP direct detection search results.

• Production at colliders: High energy colliders, like the Large Hadron Collider (LHC) [166], try to reproduce the same conditions as at the early stage of the Universe through collisions of SM particles (p-p or p-Nuclei). In this process, DM particles could be produced and escape the detection due to their neutral and weakly interacting nature. It would lead to missing energy and momentum in the final state of the collision. Up to know, experiments operating on the LHC and looking for DM candidates did not found any evidence of their production [START_REF] Buchmueller | Search for dark matter at colliders[END_REF][START_REF] Aaboud | Search for dark matter at √ s = 13 TeV in final states containing an energetic photon and large missing transverse momentum with the ATLAS detector[END_REF][START_REF] Sirunyan | Search for dark matter particles produced in association with a higgs boson in proton-proton collisions at √ s = 13 TeV[END_REF]. It must be noted that collider searches alone cannot be used to determine whether or 2 2

Chapter 2. Neutrino physics and Dark Matter direct detection not an eventual discovery of new particles is attributable to DM: the confirmation by direct or indirect detection searches is needed to claim a discovery.

• Indirect detection: In some regions of the Universe where the DM density is enhanced due to a strong gravitational potential, such as dwarf galaxies, the Sun, or the galactic center, DM annihilation can occur, producing SM particles. The The direct detection is the last of the above-mentioned approaches to search for DM particles. In this approach, earth-based experiments look for the scattering of DM particles off SM matter. Indeed, as mentioned in section 2.2.1, our galaxy is expected to move within a DM halo. Therefore, in the earth rest frame, the rotation of the sun around the galactic center will generate a constant DM wind on our planet. In this work, we will focus on the possible interaction of WIMPs with the detector target via elastic scattering off the target nucleus. This interaction is expected to generate a nuclear recoil whose energy is dependent on the WIMP and target nucleus masses and on the WIMP 2 2 2.2. Dark Matter velocity. The formula is given by:

E r = 2v 2 µ m N × cos 2 θ r (2.44)
where µ is the WIMP-nucleus reduced mass, µ = m N mχ m N +mχ , m N and m χ the target nucleus and WIMP masses respectively, v the WIMP velocity, and θ r the WIMP-nulceus recoiling angle. From equation 2.44, the recoil energy for WIMP-nucleus scattering is expected to be in the low-energy range of (1 -100) keV. The WIMP differential scattering rate as a function of the recoil energy can be written as [START_REF] Schumann | Direct detection of WIMP dark matter: concepts and status[END_REF]:

dR dE r = ρ 0 M m N m χ vesc v min vf (v) dσ χ-N dE r dv (2.45)
where M is the detector target mass, and σ χ-N is the WIMP-nucleus scattering cross-section. The description of the WIMP halo in our galaxy is necessary to esti- model is given in [START_REF] Baxter | Recommended conventions for reporting results from direct dark matter searches[END_REF]. A minimum WIMP velocity is necessary to induce a recoil on a nucleus with a given mass m N :

v min = E r m N 2µ 2 (2.46)
Above a certain escape velocity, v esc = 544 km/s [START_REF] Smith | The RAVE survey: constraining the local Galactic escape speed[END_REF], WIMPs will no longer be bound to the gravitational potential well of the galaxy. Therefore the integration is done over the v min and v esc bounds. Due to the relative motion of Earth orbiting around the Sun, annual modulation of the WIMP velocity and thus interaction rate is expected, with the rate being maximal in summer and minimal in winter 24 . This seasonal modulation of the expected signal is one of the WIMPs signatures that experiments, such as high-purity scintillator crystals like DAMA (mentioned in section 1.4), are looking for.

The interaction mechanism of WIMP with SM matter is unknown. It could be theoretically expressed in two terms: Spin-Independent (SI) interactions described by a scalar or vector effective Lagrangian, and Spin-Dependent (SD) interactions described by an axial-vector effective Lagrangian [START_REF] Schumann | Direct detection of WIMP dark matter: concepts and status[END_REF]. Both interactions are possible, then the WIMP-nucleus scattering cross-section in equation 2.45 can be expressed as [START_REF] Schumann | Direct detection of WIMP dark matter: concepts and status[END_REF]:

dσ χ-N dE r = m N 2v 2 µ 2 σ SI 0 F 2 SI (E r ) + σ SD 0 F 2 SD (E r ) (2.

47)

Chapter 2. Neutrino physics and Dark Matter direct detection with σ SI,SD 0 cross-sections for SI and SD interactions at zero momentum transfer, and F SI,SD the corresponding nuclear form factors to account for the loss of coherence at larger momentum transfers when the particle de Broglie wavelength is no longer large compared to the nuclear radius [START_REF] Schumann | Direct detection of WIMP dark matter: concepts and status[END_REF]. They are relevant only for heavy WIMP targets such as Xe, I or W. It is common for experiments searching for WIMPs to assume that DM is made only of one particle type, whose interaction in the detector can occur either via the SI or the SD mechanisms, and provide the results for the two cases independently. In the following, we will only discuss the SI case 25 . In SI interactions, the form factor F SI is commonly described by the Helm parametrisation [START_REF] Richard | Inelastic and elastic scattering of 187-Mev electrons from selected even-even nuclei[END_REF], and the SI WIMP-nucleus cross-section is

given by [START_REF] Schumann | Direct detection of WIMP dark matter: concepts and status[END_REF]:

σ SI 0 = σ n µ 2 µ 2 n (f p Z + f n (A -Z)) 2 f 2 n = σ n µ 2 µ 2 n A 2 (2.48)
The WIMP-nucleus cross-section is then converted to a WIMP-nucleon cross-section σ n , which allows for comparison of the result from different experiments employing different target nuclei. In equation 2.48, µ n is the WIMP-nucleon reduced mass, and f p,n are the WIMP-proton and WIMP-neutron contributions to the total coupling strength.

It is commonly assumed that neutrons and protons contribute equally to the scattering process (isospin conservation 26 ), leading to the second expression where f p = f n . The square of the atomic mass A 2 dependence of the WIMP-nucleus cross-section implies that experiments using heavier target nuclei expect to observe higher event rates at low momentum transfer. However, heavier nuclei are affected by the loss of coherence at larger momentum transfer, and the expected event rate drops. This is illustrated in

WIMP direct detection results

From equation 2.45 and equation 2.48, it is possible to identify the requirements that a low-background experiment searching for WIMPs must fulfill:

• A large target mass and heavy nuclei (large A) to enhance the probability of observing such rare event.

• A low energy threshold to maximize the event rate at low momentum transfer. 25 The SD case is discussed in detail in [START_REF] Schumann | Direct detection of WIMP dark matter: concepts and status[END_REF]. 26 The case of isospin-violation ( GeV WIMP in various common target materials, assuming a spin-independent WIMP-nucleon cross section σ SI = 1 × 10 -47 cm 2 . The rate for spinindependent interactions increases with A 2 , i.e., prefers heavy target materials. On the other hand, the rate for large nuclei (Xe, I, W) decreases at higher energies due to the form factor suppression. Figure and caption from [START_REF] Schumann | Direct detection of WIMP dark matter: concepts and status[END_REF].

f p ̸ = f n ) is discussed in [176].
Xenon dual-phase time projection chamber technology (TPC) is currently leading the search for WIMPs in the mass range between 10 and 1000 GeV. This technology uses heavy target nuclei (A=131 in case of xenon), it may reach an energy threshold of O(1) keV, and its scalability up to ton-scale target masses has already been demonstrated. The current best limits in this WIMP mass region are held by the LZ [START_REF] Aalbers | First dark matter search results from the LUX-ZEPLIN (LZ) experiment[END_REF] experiment, as shown in figure 2. [START_REF] Aghanim | results[END_REF]. The DarkSide-50 [START_REF] Agnes | DarkSide-50 532-day dark matter search with low-radioactivity argon[END_REF] argon dual-phase TPC also reached competitive results in the few GeV WIMP mass region. To probe lower DM candidates masses, detection technologies capable to reach even lower than O(1) keV energy thresholds must be used. The current best limit at lower than few GeV WIMP masses are held by the CRESST [START_REF] Abdelhameed | First results from the CRESST-III low-mass dark matter program[END_REF] (scintillating bolometers) and the CDMSLite [START_REF] Agnese | Search for low-mass dark matter with CDMSlite using a profile likelihood fit[END_REF] (bolometers with charge readout) experiments. However, the difficulty in increasing the target masses with such detection technology leads to worse upper limits compared to the higher WIMPs mass region.

Only one experiment has claimed positive results in the search for DM direct detection so far: DAMA [START_REF] Bernabei | First model independent results from DAMA/LIBRA-phase2[END_REF]. This experiment uses high-purity NaI scintillating crystals to search for evidences of annual modulation from the WIMP signal due to the Earth's motion around the Sun. They observed annual modulation of their event rate with a significance of 12.9 σ over 14 annual cycles. However, multiple other experiments have already excluded the DAMA result, as shown in figure 2.19. To confirm or invalidate DAMA results, several experiments such as COSINE-100 [START_REF] Adhikari | An experiment to search for dark-matter interactions using sodium iodide detectors[END_REF] and SABRE [START_REF] Antonello | The SABRE project and the SABRE proof-ofprinciple[END_REF] search (or will search) for The definition of the neutrino fog used here is discussed in [START_REF] Ciaran | New definition of the neutrino floor for direct dark matter searches[END_REF], where the gradient on the discovery limit n represents the opacity of the neutrino fog from the different sources of neutrino that could reach our detector. Therefore, CEvNS will be a dominant source of background in the next generation of xenon dual-phase TPC experiments, making the WIMP direct detection more difficult.

Simulatneous search for DM and 0νββ decay in XENONnT

In this chapter, we have introduced the interest in two of the most appealing rare-event processes, i.e., the neutrinoless double beta decay search and the WIMP direct detection search. The relevance of a Xenon target for both searches was highlighted, and the capacity of dual-phase TPC, such as XENONnT, to look for both of them simultaneously motivated the work discussed in this thesis, the search for 0νββ decay of 136 Xe in the XENONnT experiments. The XENONnT experiment and its place in the XENON program will be introduced in the next chapter.

Chapter 3

The XENONnT experiment

The XENONnT experiment has been developed by the international collaboration XENON in the context of its DM direct detection program that will be presented in section 3.1. The XENONnT detector consists in a dual-phase time projection chamber filled with xenon as a target medium, which offers great advantages for DM searches and allows for others rare events physics searches including neutrinoless double beta decay that was discussed in chapter 2. The working principle of this detection technique will be discussed in detail in section 3.2. The XENONnT detector assembly and commissioning occured at the same period of this work. The experiment started to take scientific data last year. Its design is introduced in section 3.3, while my contribution to the construction and commissioning phases is summarized in section 3.4. Finally, a focus will be made in section 3.5 on calibration strategies employed to characterize the XENONnT detector response, in view of what will be presented in chapter 4.

The XENON Dark Matter program

The The project started in 2005 with the XENON10 experiment [START_REF] Aprile | Design and performance of the XENON10 dark matter experiment[END_REF], a dual-phase TPC with an active mass of ∼ 15 kg of xenon, that allowed to demonstrate the feasibility of long-term operations with this technology and proves its efficiency by setting world-record limits on WIMP-nucleon interactions [START_REF] Angle | First results from the XENON10 dark matter experiment at the gran sasso national laboratory[END_REF][START_REF] Angle | Limits on spin-dependent WIMP-nucleon cross sections from the XENON10 experiment[END_REF]. XENON10 achieved an upper limit on the SI WIMP-nucleon cross-section of 4.5 × 10 -44 cm 2 for a 30 GeV/c 2 WIMP mass at 90% confidence level (CL).

The second generation of XENON experiments give rises in 2008 to XENON100 [START_REF] Aprile | The XENON100 dark matter experiment[END_REF],

The XENON Dark Matter program

The excess was also compatible with a possible background component not accounted for previously, originating from the β-decay of tritium. For both hypotheses (i.e., new physics or background from tritium), it was impossible to drive any conclusion due to the low available statistics in XENON1T.

In 2019, the XENON1T experiment has been decomissioned and upgraded into XENONnT, the fourth generation of the XENON program whose design will be presented in more details in section 3.3. XENONnT started to take scientific data in 2021, and already concluded a first science run (SR0), whose main goals have been the search for WIMP interactions, and the investigation of the electronic recoil excess observed at low energy by XENON1T. The WIMP analysis is still ongoing at the time of writing this thesis.

The expected sensitivity to SI WIMP-nucleon cross-section for XENONnT with an exposure goal of 20 t × y has been evaluated via Monte Carlo studies and is estimated to be 1.4 × 10 -48 cm 2 for a 50 GeV/c 2 WIMP mass at 90% CL [START_REF] Aprile | Projected WIMP sensitivity of the XENONnT dark matter experiment[END_REF]. The search for electronic recoils in the low energy region has been performed using the SR0 data [START_REF] Aprile | Search for new physics in electronic recoil data from XENONnT[END_REF]. No electronic recoil excess were observed at low energy, ruling out the BSM interpretations mentioned previously. The origin of the excess in XENON1T remains uncertain, but the most plausible explanation is that it could have been originated by the presence of tritium in the xenon target. Part of the work made in the context of this thesis, and discussed in chapter 4, contributed to those two analysis performed during SR0.

The chronology of the XENON project is summarized in figure 3.1, showing a picture of TPCs of each generation, and providing additional information regarding the operation time of the experiment, its target mass, the background rate in the region of interest (ROI) for WIMPs searches, and the SI WIMP-nucleon cross-section limit results or projections.

One of the great success of the XENON program was the demonstration of the scalability of the target mass with dual-phase TPCs and the significant suppression of the observed background rate in the detector. This allows for an improvement on the sensivity by at least one order of magnitude from one detector generation to the successive.

A picture of the XENONnT experiment in the LNGS hall B is shown in figure 3.2, with in the background the water tank, acting as passive and active shield for the heart of the experiments, i.e. the TPC. In the foreground, the support building with the experimental infrastructure, necessary to operate the detector in the required stable conditions over a long period, is visible. Next to it, on the most right part of the picture, we can see one of the xenon storage and recovery system (ReStoX2). A more detailed description of those elements is provided in section 3.3.

As presented above, all the experiments developed by the XENON Collaboration are based on the same detection technology of dual-phase TPC filled with Liquid (LXe) and Gaseous Xenon (GXe)in the next section a focus on the working principle is presented. weak decays. Furthermore, LXe features the stronger shielding power of all noble liquids thanks to its high atomic number Z = 54 and density of ρ LXe = 2.862 g/cm 3 at 177 K [START_REF] Linstrom | NIST chemistry webbook[END_REF], making it very efficient to stop penetrating radiation. This property is especially relevant for detection techniques that aim at reconstructing the position of the interaction, like dual-phase TPCs, since it allows to fiducialize part of the xenon and uses it as self-shielding. Its liquid state is also an advantage to build compact detectors with large target masses, this is fundamental to increase the experiment exposure. In addition, thanks to its relatively high boiling point temperature (178 K at a pressure of 2 bar), LXe requires a modest cryogenics system for gas liquefaction, compared to other liquid noble gases [START_REF] Aprile | Liquid xenon detectors for particle physics and astrophysics[END_REF]. ), producing scintillation light hν when decaying to the ground state [START_REF] Aprile | Liquid xenon detectors for particle physics and astrophysics[END_REF]:

Xe * + Xe + Xe → Xe * 2 + Xe Xe * 2 → 2Xe + hν (3.1)
The electron-ion pairs released by the ionization of xenon atoms can also contribute to the prompt scintillation signal through the following recombination process: On the other hand, NR loses a substantial part of their energy in the heat channel, mostly via elastic collision of xenon nuclei. Dual-phase TPCs do not detect heat, the lost of this information leads to a smaller light and charge quanta produced in NR compared to ER for the same deposited energy. It leads to a quenching of the reconstruted energy from NR. The loss of energy to the heat channel is also present in the recombination process through the biexcitonic and penning quenching process 4 , but is subdominant with respect to the contribution from atomic collisions. In the case of an ER, the energy lost in the heat channel is commonly considered negligible due to the much smaller mass of the recoiled electrons compared to the xenon nuclei in NR.

The deposited energy E can be expressed as a function of the observed light (N γ ) and charge (N e ) quanta as follow:

E = (N γ + N e ) × W L (3.3)
where W = (13.7 ± 0.2) eV/quantum [START_REF] Szydagis | NEST: a comprehensive model for scintillation yield in liquid xenon[END_REF] is the average energy required to generate a photon or electron-ion pair, and L is the Lindhard quenching factor used to account for the loss of energy to heat. In case of an ER this factor is negligble (L ∼ 1), while for a NR its impact is dominant (L ∼ 0.1 -0.2) [START_REF] Lindhard | Range concepts and heavy ion ranges (notes on atomic collisions, ii)[END_REF]. This quenching factor is energydependent, and only semi-empirical approaches are available to estimate it for a xenon target. Notably, the Noble Element Simulation Technique (NEST) [START_REF] Szydagis | NEST: a comprehensive model for scintillation yield in liquid xenon[END_REF] is commonly used in xenon-based experiments to model light and charge yields from ER and NR (as a function of the energy and electric fields applied), as well as the quenching factor L.

The energy reconstruction in a xenon dual-phase TPC relies on the measurements of the light and charge quanta produced in the interaction. The working principle of such a detector will now be introduced.

Dual-Phase TPC Working Principle

The working principle of a dual-phase TPC is depicted in figure 3 3.2) were optimized to maximize the optical transparency of the electrodes and that were stretched across massive frames by means of oxygen-free high conductivity copper (OFHC) pins. In the case of the anode (gate) electrode, four (two) additional 304 µm-diameter perpendicular wires were installed to minimize sagging, as shown in figure 3.9. Furthermore, two concentric cages of field shaping electrodes made of OFHC were installed around the TPC to improve the field's uniformity [START_REF] Aprile | Field cage for the XENONnT detector[END_REF]. The electrodes were designed to operate the TPC at a drift field of ∼ 200 V/cm and an extraction field of ∼ 8 kV/cm. Nevertheless, as it will be discussed in section 3.4, this field goal was not achieved for the first science run of XENONnT. The level of the liquid-gas interface in the TPC is controlled by pressurizing the xenon gas in a stainless steel diving bell and is kept stable 5.1 mm above the gate electrode.

searches. Cryogenic distillation columns 9 are used to supress their concentration in the xenon target. In XENON1T a krypton distillation column was developed [START_REF] Aprile | Removing krypton from xenon by cryogenic distillation to the ppq level[END_REF]

Slow Control and Data Acquisition Systems

The different sub-systems of XENONnT presented previously are constantly monitored by the slow control (SC) system. It follows the same architecture used in XENON1T [START_REF] Aprile | The XENON1T dark matter experiment[END_REF][START_REF] Cardoso | Experience with a slow control system based on industrial process control hardware and software for the XENON1T dark matter search[END_REF] and is based on industry-standard control hardware (PACs: Programmable Automation Controllers) and software (Cimplicity SCADA). The SC includes automatic operations and manual control to be applied to the different sub-systems remotely (from PMT calibration to electrodes HV). All the monitored parameters are regularly stored in a Proficy Historian database that can be used to define and trigger an alarm (e.g., parameter out of range, equipment failure, etc.) that is transferred to the relevant users.

The data acquisition system (DAQ) used to readout all XENONnT PMTs signal (TPC, nVeto, and µVeto) have been updated compared to the XENON1T DAQ in order to be able to handle the increased number of PMTs and allow a quasi-triggerless acquisition logic, except for the per-channel digitization thresholds [START_REF] Aprile | The triggerless data acquisition system of the XENONnT experiment[END_REF]. Among the various evolution of the DAQ between the two detector generations, it is worth mentioning the installation of custom-developed dual-gain amplifiers featuring a high-gain (OE10) and a low-gain (OE0.5) output [START_REF] Wulf | Direct Dark Matter Search with XENON1T and Developments for Multi-Ton Liquid Xenon Detectors[END_REF], used to amplify the TPC's PMTs signals. The low-gain amplification improves the energy and position reconstruction for high-energy signals by 9 The distillation process is based on the difference of vapor pressures of the two components in an ideal binary mixture, in our case krypton/radon and xenon.

Construction and commissioning

minimizing the saturation of the digitizers. The PMTs amplified signals are then digitized by V1724/V1730S modules, whose outputs are fed to reader servers that write the data to a common storage disk. The data processing framework strax(en), presented in section 4.1, analyses those data and build higher-level data structure and transfer them to different storage site (various copy, to avoid any data loss).

Construction and commissioning

The installation of XENONnT started in parallel to the decommissioning of XENON1T in March 2019, with the upgrade and commissioning of the various sub-systems presented previously. Prior to the TPC assembly, thorough cleaning of its elements was a mandatory step to remove small particulates that might compromise the target purity. Those operations were carried on in a cleanroom dedicated to the XENON operations in the aboveground laboratory at LNGS. In the context of this thesis, several periods of shifts were performed on-site, one of which occurred in January 2020. During this period, I contributed to the cleaning of two elements of the TPC, i.e., the five parallel wire grid electrodes and the PTFE pillars, as illustrated in figure 3.12. For a complete description of the cleaning procedure for the various elements of the TPC, the reader must refer to [START_REF] Aprile | Material radiopurity control in the XENONnT experiment[END_REF]. with a total livetime of 97.1 days. The SR0 data analysis performed during this thesis will be discussed in chapter 4.

Detector Calibration Strategies

Understanding and characterizing the detector response to different particle interactions is essential to exploit the acquired data properly, and this is the purpose of the various calibrations carried out in XENONnT. In particular, dedicated calibrations are necessary to determine the interaction type (ER/NR), reconstruct position and energy of the interaction, and to correct the measured signals to account for detector effects. However, operating a low background experiment implies various constraints on the calibration techniques that can be classified into two categories: internal and external calibrations.

Internal calibration

Internal calibration: Injecting radionuclides directly into the xenon target allows for a uniform distribution of the calibration source and thus a better characterization of the active volume of the TPC. However, this method cannot be applied to all calibration sources but only to those with a sufficiently fast decay time to allow rapid resumption of scientific data taking (i.e. data that will be later use for rare events searches).

In XENONnT three radioactive gaseous sources are used to calibrate the detector, namely 83m Kr, 220 Rn, and 37 Ar. They are mixed to the GXe through an emanation chamber placed in a dedicated circulation loop, called calibration box and shown in figure 3.14, that are connected to the rest of the GXe recirculation system.

Calibrations with 83m

Kr is performed via the emanation of a gaseous 83 Rb source directly into the TPC. The 83 Rb decays into 83m Kr with a half life of 86.2 days and a branching ratio of 77.9%. The Kr83m subsequently emits two successive mono-energetic lines at 9.4 keV and 32.2 keV, close to the energy ROI for WIMP search, with a half-life of 1.83 h. This calibration source is a milestone in the XENONnT data analysis: it is used to study and correct the measured signals for the detector effects that impact the measurements of all interactions, as well as to reconstruct the events position and energies. The procedure definition and optimization to properly select 83m Kr events during dedicated calibration runs was one of my responsibility during SR0 and it will be discussed in detail in chapter 4. 220 Rn is performed via the emanation of an electrodeposited 228 Th gaseous source directly into the TPC. The 220 Rn decay chain is shown in figure 3.15: 220 Rn emits β, γ, and α particles that can be used to calibrate the detector for different particle interactions. Notably, it offers a β-spectra from 212 Pb, that decay to the ground state characterize the ER band, represented in the upper plot of figure 3.6. The 212 Pb has the shortest half-life of the decay chain and thus dominates its mitigation in the xenon target.

Calibrations with

Its activity is reduced by a factor 6 × 10 4 within one week [START_REF] Aprile | The XENON1T dark matter experiment[END_REF], a non-negligible time that prevents its use for regular calibration during the science run. This calibration is usually performed at the beginning or the end of the science run (or both).

Calibrations with 37 Ar have been employed for the first time by the XENON collaboration in XENON1T and currently used for XENONnT. This calibration source allows to study low energy ER interaction close to the energy threshold of the experiment. It is caracterized by the emission of two monoenergetic lines at 0.27 keV and 2.8 keV [START_REF] Aprile | Calibration of XENON1T with an internal 37 ar source[END_REF].

With a rather long half-life of 35.0 days, the calibration can only be made at the end of the science runs, and the remaining 37 Ar isotopes within the TPC can be removed using the Rn distilation column.

In addition to the three calibration sources presented above, background components intrinsic to the xenon target can also be used for calibration purposes. This is the case for 222 Rn emanated from the materials, whose contaminants remains present at the trace level after xenon distillation. Metastables states of xenon isotopes originating trough neutron capture after having performed external neutron calibrations, such as 129m Xe and 131m Xe, can also be used to calibrate the detector. These intrinsic sources of calibrations were exploited in the context of this work, and will be discussed in section 4.3.

External calibration

External calibration: An alternative to internal calibrations consists in placing external sources outside of the TPC, usually near the cryostat, in order to locally characterize specific regions of the detector. This technique can be used also to calibrate the neutron veto. The main disadvantage in using external calibrations sources in large experiments like XENONnT, is the low statistic of events reaching the central part of the detector: this is due to the xenon's high shielding power.

Three different systems are used in XENONnT to perform external calibrations. They are illustrated in figure 3.16. Highlighted in purple, the L-shaped beam pipe can provide collimated neutron beams produced by a pulsed high-energy neutron generator with a maximum rate of 10 7 n/s. To realize low-energy neutron calibration that can be used to caraterize the NR band close to the energy threshold (see bottom part of figure 3.6), a heavy water (D2O) volume can be lowered together with the neutron generator. An I-belt structure, depicted in blue, is used to move a Tungsten collimator, hosting a 88 Y -Be source, vertically along the cryostat. This source emits neutrons (low-energy) and γ to calibrate the detector along a specific azimuthal angle. Finally, two independent 1" stainless steel U-tubes, highlighted in red and green, run around the cryostat at different heights.

Small external sources can be guided through the tubes and allow the characterization of the TPC and nVeto at different z and azimuthal angles. Different sources can be used to calibrate the detectors with neutrons from an 241 AmBe source, as well as high-energy gamma from 228 Th, or 137 Cs sources.

The common bottleneck of all the external calibrations is the difficulty in characterizing the central part of the TPC due to the xenon high-shielding power. This is compensated by taking calibration data over a long period to reach the required statistics. However, in order to avoid reducing significantly the scientific data livetime these calibrations are usually performed at the beginning or the end of the science run.

Calibration campaign

Chapter 4

Signal reconstruction and monitoring during XENONnT first science run

The first science run (SR0) of XENONnT began on the 3rd of May, 2021, and ended on the 4th of January, 2022, when the detector was operated stably in the SR0 conditions introduced in section 3.4. The chronology of SR0 is shown in figure 4.1, where the periods dedicated to the calibration data acquisition discussed in section 3.5 are overlayed and represented by different color bands. The scientific data acquisition, also referred to as background data, corresponds to periods during which no calibration sources have been used and that are used for rare events searches. To minimize bias during data analysis, the regions of interest of each physical search are blinded, i.e., inaccessible to analysts during the development and optimization of the specific analysis. The collected blinded data in SR0 span over a period between the 6th of July, 2021, and the 10th of November, 2021. Three different blinding regions have been defined so far in SR0 depending on the physics channel: one for the WIMPs search at low energy NR, one for the ER search at low energy (low-ER), and the last one for 0νββ decay search at high energy ER. The evolution of the blinded data livetime during SR0 is shown in figure 4.1 as a solid black line. In addition to the calibration periods, two weeks of tritium-enhanced data were taken in November (Getter bypass mode), whose purpose was to test the tritium hypothesis as responsible for the XENON1T low-ER excess [START_REF] Aprile | Excess electronic recoil events in XENON1T[END_REF]. These data are not of interest in the context of this thesis and, thus, will not be discussed further. The periods where the detectors were not operated in SR0 dondition, due to maintenance operations or hot-spot 1 appearance, are shown with grey bands.

The priority for SR0 in terms of physics goals was given to the WIMP 2 and low-ER searches [START_REF] Aprile | Search for new physics in electronic recoil data from XENONnT[END_REF]: they are the first two analyses performed with XENONnT data. The work presented in this chapter has been developed specifically to study the detector per-1 Single electron bursts introduced in section 3.4. 2 The results of the WIMP search with XENONnT SR0 data were not published when writing this manuscript but should be released in the coming months.

Signal Reconstruction with the Strax(en) Analysis Frameworks

For this reason, in this chapter I decided to follow, the structure of the paper: the content presented in the following sections includes details that go beyond my personal contributions. Nevertheless, an emphasis on my work will be made at the moment of their presentation, while the work primarly performed by others will also be clearly stated.

Signal Reconstruction with the Strax(en) Analysis Frameworks

A new analysis framework has been developed in XENONnT to handle the processing of the continuous datastream recorded by the triggerless DAQ systems introduced in section 3.3.5. It employ the strax [START_REF] Aalbers | [END_REF] and straxen [218] python based processing frameworks3 , hereafter mentioned as strax(en) for simplicity, that allow for fast live processing of data with a rates of O(10 -100) MB/s/core [START_REF] Aprile | The triggerless data acquisition system of the XENONnT experiment[END_REF]. Online monitoring of the detector performance can be applied on high-level data thanks to the quick processing time after the light detection by the PMTs, estimated to be of O(10) s. The purpose of strax(en) is to process the measured PMTs digitized pulses recorded by the DAQ system and determine the properties of the signals to build higher-level structures, called datatype, that are used to reconstruct events. An event is defined by a pair of S1 and S2 signals originating from a physical interaction in the TPC.

In the following, we will only present the processing steps for the signal recorded by the TPC PMTs. Muon-and neutron-veto PMTs are also handled by straxen but will not be discussed here. Three main datatypes exist, from lowest to the highest level: the raw-records corresponding to the PMTs traces recorded without any processing applied, the peaks that correspond to S1 and S2 signals reconstructed from the raw records, and the events resulting from the pairing in time of the peaks. High-level datatypes are built from the lower-level ones via several processing functions called plugins. It leads to a modular and flexible structure of the data processing, allowing for reprocessing of some specific datatype instead of a full reprocessing of the data when needed. The figure 4.2 is an infographic depicting the data processing workflow used for the SR0 of XENONnT.

We will now overview the steps that allow building events from the PMTs measurements.

1. Hit Finding: PMTs pulses exceeding the building threshold, usually similar to the digitizer trigger threshold of 15 ADC, are baseline-substracted, inverted, and integrated to form hits.

2. Peaklets Construction: Hits are then clustered in time with a gap time threshold of 700 ns. The groups of hits sorted by time are then summed over all PMTs with a 10 ns sampling to build an intermediate level of data: the peaklets and lone hits. Peaklets correspond to a group of hits from multiple PMTs, while lone hits correspond to hits detected in a single PMT. The time gap threshold used to split the peaklets was defined in order to reconstruct the different building elements of the S1 and S2 signals while minimizing the contamination from other types of signals such as single electrons (SEs) and afterpulses (APs), defined hereafter 4 . The amplitude of the hits constituting peaklets samples are converted to photoelectron (PE) units using the information on the individual PMTs gains (ADC count per PE). The total amplitude of each sample of peaklets is given by the sum of their areas.

Definitions

Single electrons (SE) refers to lone electrons produced primarly via the photoelectric effect from photons emitted by a primary S2 in the gas phase that goes back into the LXe phase and interacts with the impurities or materials (mostly the gate electrode). Those electrons are extracted in the GXe phase and produce scintillation light via electroluminescence. While being a potential source of bias in the S2 signal reconstruction and background for low S2 searches, SE can be assimilated to the building blocks of S2 signals (electron cloud) and thus offer a unique opportunity to characterize the scintillation gain from individual electrons. This is a necessary information to convert the S2 signal areas into the observed number of charge.

Afterpulses (AP) defines any PMT pulses that originate from inside the PMT itself and is delayed to the initial pulse that created it. Among the main source of afterpulses, we can mention the ionization of residual gases present in the PMT tube by a primary photoelectron. The produced ions positively charged are then accelerated back towards the photocathode leading to the delayed emission of photoelectrons. The delay time between the primary pulse and the afterpulse depends on the mass-to-charge ratio of the ionized atoms and the PMT bias voltage. In XENONnT PMTs, most of the AP are due to He + , Ar + , and Xe + ions, whose delay time ranges from ∼ 500 ns up to ∼ 3 µs.

Peak Construction:

The second step in building the peaks from the PMTs pulses consists in the peaklets classification. Based on their properties they are separated 4

We can also mention the dark count that is originating from thermionic emission of electrons from the photocathode or the first dynodes, inducing a signal without any incident light. The dark count rate is strongly dependent on the temperature and, therefore, can be significantly reduced to a negligible level (few Hz) in low-temperature environments, such as xenon operation conditions in dual-phase TPC.

Event Building:

The event building has been constructed in order to define events containing an S1 and S2 pair but also S2-only events. Any S2 with an area above 100 PE, and less than eight peaks with at most 50% of its area in a 100 ms window (to reduce noisy events), would trigger an event. The time region of an event is defined as 2.45 ms before and 0.25 ms after the triggering S2 peaks, to exceed the maximal driftime expected in XENONnT with the SR0 drift field. If an S1 peak is found in this time window before the S2 peaks, they are both paired together. If multiples S1 and S2 peaks are present in the event time window, only the largest peaks are paired together. The properties of only the two largest S1s and S2s are saved at the event level. An example of an event waveform is shown in figure 4.3.

Definitions

The Peak(let) classification algorithm uses the peak(let) properties defined below to classify them either as S1, S2 or unknown signals.

• Area: Integral of the peak(let) samples amplitude in PE.

• Rise time: Time to reach 10% of the peak(let) area in ns.

• Tight coincidence: The number of PMTs contributing within a 100 ns window centered on the peak(let) maximum sample.

• Area fraction top (AFT): Fraction of the peak(let) area measured by the top PMT array.

Step Step 2: S2 classification Remainings peak(let)s with a 3-fold coincidence with other PMTs are classified as S2 signals.

Step 3: Unknown classification Finally, all peak(let)s neither classified as S1 nor as S2 are defined as unknown signals.

The properties of the different levels of datakind (pulses, peak(let)s, and events) are derived with dedicated plugins, as mentioned earlier. The higher-level type of data inherits from some of the properties of the lower-lying one when they are relevant 5 . In total, ∼ 120 variables are available at the event level [218]: from the timing information of the peaks (start, end, center time, etc.), the shape characteristics (rise time, widths, etc.) and the number of contributing PMTs for each peak, to the reconstructed position of events.

The latter is derived in two steps, as introduced in section 3.2.2. The interaction depth is given by the difference between the center times of the main S1 and S2 peaks in an event.

Three different position reconstruction algorithms were used to infer the (x,y) coordinate from the S2 hit pattern on the top PMT array: a multilayer perceptron (MLP), a convolutional neural network (CNN) and a graph convolutional network (GCN). The three Processing of the PMT traces with a hit finding algorithms to build hits.

1. Cluster hits in groups with a time gap threshold 2. Sum over all PMTs to build peaklets or lone hits.

1. Peaklets are then iteratively splitted with a Natural break algorithms to differentiate S1 and S2 candidates. neural networks were trained with light patterns obtained from optical simulations that include detector effects such as PMT gain, optical detector properties, missing PMTs, etc.

The MLP algorithm has shown the best performance: a spatial resolution, ranging from ∼ 0.25 cm for high energy S2s (O(10 4 ) PE) in the radial center of the detector, to ∼ 3 cm for low energy S2s (O(10 2 ) PE) near the edge of the sensitive volume has been reached6 .

For this reason, the MLP algorithm has been chosen as the baseline to reconstruct the signal position. Therefore, in the following, when reconstructed positions will be discussed, they will correspond to the MLP-based ones. All the informations discussed in this section, will be used to reconstruct all data, including the calibration ones. As it will be presented in the next sections, those data are used to monitor the detector response during data taking periods and also to correct the measured S1 and S2 signals for detector effects like field distorsion, electron captured by impurities within the xenon target and others. Corrected data will then be used to infer the interaction type (NR or ER), its energy and position.

83m Kr Calibration and Signal Correction

The corrections of measured S1 and S2 signals in XENONnT are derived from the study of calibration data, mostly from the 83m Kr internal calibration source. The characteristics and advantages of this calibration source and the definition of selection criteria necessary to exploit those events are detailed in section 4.2.1. Those selection criteria are then used to build most of the signal corrections required to account for various detector effects affecting the signal measurements in our detector, as presented in section 4.2.2.

83m Kr events selection

As introduced in section 3.5. [START_REF] Wittweg | Second-Order Weak Decays in XENON1T and Future Xenon Time Projection Chambers[END_REF], with transition path from [START_REF] Manalaysay | Spatially uniform calibration of a liquid xenon detector at low energies using kr83m[END_REF] and updated half-life from [START_REF] Mccutchan | Nuclear data sheets for A = 83[END_REF].

Based on the above considerations, we can distinguish three topologies of 83m Kr events, depending on the number of reconstructed distinct S1s and S2s as illustrated in figure 4.5.

• Events with 2 S1s (32.1 and 9.4 keV) and 2 S2s (32.1 and 9.4 keV), so-called KrDou-bleS1S2 events (Top sketch in figure 4.5). This population is the most challenging to reconstruct due to the difficulty of reconstructing two distinct S2s with a time separation of O(100) ns while having O(1) µs widths. Its selection was investigated in the context of this thesis using XENONnT SR0 data, but due to the low drift field and the splitting and clustering algorithms used, it was not possible to isolate such topology of events (they will not be discussed any further in the following).

• Events with 2 S1s (32.1 and 9.4 keV) and 1 pile-up S2 corresponding to the sum of the two Kr83m transitions (41.5 keV), so-called KrDoubleS1SingleS2 events (Middle sketch in figure 4.5).

• Events with 1 pile-up S1 (41.5 keV) and 1 pile-up S2 (41.5 keV), so-called KrSin-gleS1S2 events (Bottom sketch in figure 4.5).

A dedicated naming convention is used to refer to 83m Kr events, where the largest S1 Kr events is also depicted with their corresponding description in the caption. Both figures were made using data with an equivalent livetime of 45 hours. The difference between calibration and background events is evident, but the selection of 83m Kr events is not straightforward due to the different topologies of events mentioned previously. It requires the definition of dedicated selection criteria for each population. In the following I will present the Kr83m signal properties and motivate the definition of boundaries applied on several variables used to select the different events topologies. The full list of cuts applied to select a specific population will be provided at the end of each section.

In the following, we will present the methodology used to define selection criteria aiming to isolate the KrSingleS1S2 population and the KrDoubleS1SingleS2 population, which will be referred to as KrDoubleS1 for simplicity from now on, using only non-corrected information. The goal of those selection criteria is not to isolate as many 83m Kr events as possible, but rather to select as many 83m Kr events that do not show any clear evidence of reconstruction bias as possible. The The selection will then focus first on the S1s properties (or variables) to isolate 83m Kr events, while S2s variables will be studied afterward. Numerous signal properties were The result of the KrSingleS1 selection criteria is shown in figure 4.13 without additional quality cuts on the left panel. The same parameter space with a FV cut applied9

in addition to the KrSingleS1 selection criteria to remove events affected by edge effects, is shown on the right panel. These selection criteria are able to isolate a clean sample of KrSingleS1 events with a total acceptance of ∼ 50 %, allowing us to gather high event statistics.

83m Kr Double S1 population

The selection of the KrDoubleS1 population will follow the same procedure that was used to define the KrSingleS1 selection criteria in section 4.

Field distortion correction

Despite efforts to produce a homogeneous electric field in the TPC, its distortion is inevitable due to the presence of repulsive negative charges on the PTFE wall that confine the TPC, as shown in figure 4.19. This field inhomogeneity has two main consequences:

• Non-uniformity of the light and charge quanta production at a given energy due to the field dependence of the recombination process.

• Distortion of the field lines followed by the charges when drifting towards the GXe phase, resulting in a disagreement between the observed (x, y) position of the S2 signals and the true position of the interaction point.

The internal 83m Kr calibration source, expected to be homogeneously mixed with the xenon target, allows us to study the impact of the field distortion on the events position was also observed in XENON1T and attributed to the charge accumulation in the PTFE reflectors, not pillars [START_REF] Aprile | XENON1T dark matter data analysis: Signal reconstruction, calibration, and event selection[END_REF]. Accordingly, the XENONnT field cage was designed to be in contact with both PTFE pillars and reflectors to evacuate the accumulated charge. Nevertheless, it seems that the charge accumulation effect is still persistent 10 in XENONnT for PTFE pillars due to their larger thickness. This effect is stronger for events originating at the bottom of the TPC as shown on the (r 2 obs , z obs ) space in the bottom left panel of figure 4.20.

A three-dimensional data-driven field distortion correction (FDC) map can be derived from 83m Kr data under the assumption that 83m Kr events are uniform in r 2 true . Using both KrDoubleS1 and KrSingleS1 population 11 , the TPC volume is divided into 180 and 80 slices in both azimuthal angle ϕ obs , and z obs directions, respectively. In each slice, event radial positions are corrected such that they are evenly spaced in the r 2 corr space, considering that the 99.4% percentile of the corrected radial distribution must coincide 10 The effect is nevertheless less strong than in XENON1T.

11

We are interested in the reconstructed position, not deposited energy; therefore, both populations can be used.

trodes. Furthermore, the xenon liquid-gas interface also acts as a reflective plane 12 .

The light reflection increases the probability of the photons being absorbed, affecting the measurement of the light quanta production. The TPC was designed to minimize this effect as much as possible, as presented in section 3.3.1, but part of the light can still be lost. The fraction of generated photon reaching the photocathode of a PMT is noted ϵ S1 LCE and is referred to as S1 light collection efficiency (LCE).

• In order to estimate the proportion of photons reaching the photocathode that will effectively produce a PE, the quantum efficiency of the PMTs noted ϵ QE must be taken into account. Furthermore, the probability of double PE emission (DPE), noted p DPE , where two PE are occasionally emitted when one photon hits the PMT photocathode [START_REF] Paredes | Response of photomultiplier tubes to xenon scintillation light[END_REF][START_REF] Faham | Measurements of wavelength-dependent double photoelectron emission from single photons in VUV-sensitive photomultiplier tubes[END_REF], must be considered. Finally, the collection efficiency of PE within the PMT, noted ϵ CE , can also further reduce the number of photons detected.

Accordingly, the relation between measured S1 signals and light quanta produced, noted N γ , can be expressed as:

S1 = N γ • ϵ S1 LCE (x, y, z) • ϵ QE • ϵ CE • (1 + p DPE ) (4.1)
Relative light yield map: We expect that the measurements of S1 signals will depend on the position of the interaction in the xenon target. This is due to the S1 LCE of the TPC but also to the field inhomogeneity introduced in section 4. • Once the electrons are extracted in the GXe phase they will generate photons through the electroluminescence process, whose average number produced per extracted electrons corresponds to the secondary scintillation gain (or SE gain), noted G SE . This gain depends on the extraction field and the gas gap between the xenon liquid-gas interface and the anode. This process is also at the origin of a spatial dependence.

cS1 = N γ • ϵ S1 LCE • ϵ QE • ϵ CE • (1 + p DPE ) (4.
• Similarly to the S1 signal, the fraction of photons generated in the electroluminescence process that reaches the PMT photocathode, denoted as ϵ S2 LCE and referred to as S2 LCE, is also affected by light propagation effects. Nevertheless, since S2s photons are only produced in the thin gas gap between the liquid-gas interface and the anode, this effect does not require a three-dimensional correction like in the S1 signal case. Instead a 2D correction map on the (x, y) plane can be used.

• Finally, photons reaching the PMTs photocathode are subject to the same PMT response variation induced by the quantum and collection efficiency and probability of DPE emission, as introduced in the S1 correction case.

Based on the above-mentioned detector effects and assuming a perfectly stable detector, it is possible to express the relation between measured S2 signals and generated charge quanta (N e ) as follows:

S2 = N e • f EL (t D ) • ϵ ext (x, y) • G SE (x, y) • ϵ S2 LCE (x, y) • ϵ QE • ϵ CE • (1 + p DPE ) (4.3)
Two independent spatial dependencies are observed: along the z axis due to the presence of impurities in the LXe, and in the (x, y) gas amplification plane induced by the S2 LCE, EE efficiency, and SE gain spatial variation. Nevertheless, the XENONnT TPC was operating dynamically during SR0, with two major phenomena that induce a time dependence on some physical process of the S2 generation listed previously.

Light and Charge Yields monitoring

The corrected areas of the S1 and S2 signals allow us to determined the light (LY) and charge (CY) yields, defined as the number of measured PE per deposited energy (in keV):

LY(E) = cS1 (PE) E (keV) CY(E) = cS2 (PE) E (keV) (4.6)
These properties are essential to reconstruct the deposited energy in the detector, as it will be discussed in section 4. • Measurements of the LY and CY time stability with the internal 83m Kr calibration data.

• Development of a global analysis framework that allows to monitor LY and CY during the whole science run, encompassing the studies of all the relevant calibration sources performed by other analysts.

• Coordination of the LY/CY stability analysis group.

The methodology used to measure the LY and CY will be described in section 4.3.1,

A (cS1, cS2) = A 0 × exp - f 1 (cS1, cS2) 2a 2 - f 2 (cS1, cS2) 2b 2 + B 0 (4.7)
where A 0 is the peak amplitude, B 0 is a term modeling a possible constant background contribution, a and b correpond to the rotated standard deviations in cS1 and cS2, and f 1/2 are functions dependent on cS1 and cS2 with the form:

f 1 (cS1, cS2) = [(cS1 -µ S1 ) × cos θ -(cS2 -µ S2 ) × sin θ] 2 f 2 (cS1, cS2) = [(cS1 -µ S1 ) × sin θ + (cS2 -µ S2 ) × cos θ] 2 (4.8)
with µ S1/S2 , the mean cS1 and cS2, and the ellipse rotation angle θ. The fit function is illustrated in figure 4.27 with the different parameters mentioned above. The LY and CY can be derived from the peaks means µ S1/S2 divided by the energy, as follow:

LY(E) = µ S1 E CY(E) = µ S2 E (4.9)
The results for figure 4.27 is LY = 9.4582 ± 0.0008 PE/keV and CY = 184.42 ± 0.03 PE/keV. The poor goodness of fit is due to an asymmetric cS2 distribution with tails towards a large area leading to the "hat" in the ellipse. This population is most likely due to non-perfect S2 corrections and the extraction of trapped electrons at the liquid-gas interface released when the electron cloud from 83m Kr decay reaches the gas amplification phase. This effect is still under investigation, but it does not significantly impact the LY and CY stability monitoring. The same method described in this paragraph can be applied to other mono-energetic sources, as the one presented in section 4.3.2.

LY Measurement with KrDoubleS1 population:

In the case of the KrDoubleS1 population, the same methodology used for the KrSingleS1 population (and more in general for mono-energetic lines) cannot be applied since for each events containing two distinct S1s corresponding to the 32.1 keV and 9.4 keV transition, a unique S2 of 41.5

keV (corresponding to the pilup of the two S2 signals) will be reconstructed. Therefore another methodology needed to be developed in order to measure the LYs at those two energies 19 : it uses the cS1 a and cS1 b amplitudes, as detailed below. In order to mitigate the fluctuations that could arise from remaining reconstruction bias of the KrDoubleS1 events (from contamination of AP, for example), the following procedure has been used: • The cS1 a (32.1 keV) peak is the first and, therefore, less affected by the contamination from AP that could bias the LY measurement. This allows to determine a time range for the linear fit, starting at 450 ns 20 . At larger delay time between S1s, (∼ 1100 ns) fluctuations can be seen in the top panel of

Signal stability studies

In XENONnT, four internal sources of calibration, offering mono-energetic lines over a wide energy range, were used to monitor the LYs and CYs.

• The 83m Kr calibration data allow monitoring, on a bi-monthly basis, the LY at 9.4 keV, 32.1 keV, and 41.5 keV, as well as the CY at 41.5 keV, as presented in the previous section.

• The 222 Rn alphas allow monitoring the LY and CY at 5.5 MeV from the emission of an α particle 21 . Due to the constant presence of this isotope in the xenon target (caused by the emanation from the materials), this alpha decay has been used to monitor the LY and CY daily. In that case, the standard method of 2D gaussian fit on the (cS1, cS2) space has not been used due to the poor statistics. Instead, the mean of the two signals distribution was used as an estimator of LY and CY. This choice was motivated by the fact that we are more interested in the evolution of those properties than their actual values, and the 222 Rn alpha is the only calibration source that allows performing such a frequent measurement during the whole SR0.

• The 129m Xe and 131m Xe activated lines, are generated after neutron and AmBe calibrations through the (n, γ) process. The decay of those metastable states allow to measure the LYs and CYs at 236 keV and 164 keV respectively. Nevertheless, the low statistics collected in SR0 did not allow to use this source for monitoring purposes during the whole science run but only for a specific period corresponding to a calibration taken in June 2021.

• The high energy gamma lines, originating from materials and reaching the sensitive volume of the detector, can also be used to monitor the LYs and CYs at different energies. During SR0, five gamma lines were studied: 60 AmBe calibration period in June. An anti-correlation between the LY and CY variation is also clearly visible. This behavior is due to the SE gain and EE efficiency corrections that exhibit a time and spatial dependence, which is not perfectly modelled in this period.

In addition to the time stability study, I also initiated a study of the spatial stability of LY and CY using 83m Kr data that I will not detail here, and that has been completed by a second year PhD student of the group. The current conclusions we can drive on this study are that the LY was homogeneous in the whole TPC (< 1% variation) while the CY shows a z-dependence whose largest amplitude is < 4%. This study indicates that improvements in the corrections (especially for S2s) can be achieved in the future. Furthermore, another study aiming to investigate the possible sources of systematic uncertainty on the LY and CY measurements recently started under my supervision and is carried on by a first year PhD student of the group.

Energy reconstruction

The reconstruction of the deposited energy during an interaction is based on the measurements of the cS1 and cS2 signals, as introduced in section 3.2.2 and recalled below:

E = W × cS1 g 1 + cS2 g 2 (4.10)
where g 1 and g 2 are the photon detection efficiency and charge amplification factors, respectively. Those parameters can be derived from the measurements of LY and CY from mono-energetic sources at different energies as presented in section 4.3.1. Indeed, by using equation 4.6 in equation 4.10, we can express the linear dependency between the LY and CY as a function of g 1 and g 2 , as shown in equation 4.11:

CY = - g 2 g 1 LY + g 2 W (4.11)
In SR0, nine mono-energetic lines were used to extract g 1 and g 2 . In addition to the 83m Kr, 129m Xe, 131m Xe, 40 K, and 60 Co lines also used for the LY/CY monitoring presented in section 4.3.2, three additional lines were studied:

• the 12 C gamma line at 4438.9 keV emitted during AmBe calibration via the (α, n) reaction on Be within the source,

• the 2 H gamma line at 2224. In XENON1T, these improvements led to the world-leading energy resolution at Q ββ1 of 0.8% (σ/E) in a xenon dual-phase TPC [START_REF] Aprile | Energy resolution and linearity of XENON1T in the MeV energy range[END_REF]. Based on this promising result, a sensitivity projection study for 0νββ decay search in XENONnT has been performed and will be presented in this chapter. The context of the analysis will be discussed in section 5.1. The signal and background models will be reported in sections 5.2, 5.3, and 5.4, respectively. In section 5.5, the inference framework used in this study is shown. Finally, the result of the projected sensitivity of 0νββ decay of 136 Xe for XENONnT is reported in section 5.6. Experiments [START_REF] Aprile | Double-weak decays of 124 Xe and 136 Xe in the XENON1T and XENONnT experiments[END_REF], for which I was appointed as one of the corresponding authors.

This analysis results from a collaborative work performed in collaboration with others

Context of the 0νββ decay projection study for XENONnT

The XENONnT projected sensitivity study for 0νββ decay of 136 Xe is part of a more significant analysis effort of the XENON Collaboration dedicated to studying double-weak decays in Xenon dual-phase TPC. Three studies have been performed, whose goals and main results are the following:

• Extended Search for Two-Neutrino Double-Electron Capture in XENON1T:

The observation of the two-neutrino double-electron capture in 124 Xe is one of the major results of the XENON1T experiment that has been obtained using 177.7 live time days of data. It was the first observation of a second order process with the longest directly measured half-life of of 1.8 × 10 22 years [START_REF] Aprile | Observation of two-neutrino double electron capture in 124 Xe with XENON1T[END_REF]. An increased exposure and improvements in the signal selection and background modeling allowed an extended search, resulting in a signal significance of 7 σ [START_REF] Aprile | Double-weak decays of 124 Xe and 136 Xe in the XENON1T and XENONnT experiments[END_REF].

• Neutrinoless Double Beta Decay Search using XENON1T Data: The development of an analysis has been performed for the first time by the XENON collaboration using blinded data from the XENON1T experiment. The result is compatible with the background-only hypothesis and allows to put a lower limit on the half-life of 136 Xe to the 0νββ search of T 0νββ 1/2 > 1.2 × 10 24 yr at 90 % C.L. [START_REF] Aprile | Double-weak decays of 124 Xe and 136 Xe in the XENON1T and XENONnT experiments[END_REF]. This result serves as a proof of concept to demonstrate the feasibility of such analysis using dual-phase TPC detectors.

• Neutrinoless Double Beta Decay Search Projection Study for XENONnT:

Using a detailed MC simulation it has been possible to estimate the half-life sensitivity of XENONnT to the 0νββ decay of 136 Xe. Despite not being competitive with experiments dedicated to the 0νββ search like EXO-200 [START_REF] Anton | Search for neutrinoless double-β decay with the complete EXO-200 dataset[END_REF] and KamLand-Zen [START_REF] Gando | Search for majorana neutrinos near the inverted mass hierarchy region with KamLAND-Zen[END_REF] , XENONnT can still reach a good sensitivity of the order of T 0νββ 1/2 > 2.1 × 10 25 yr at 90 % C.L., assuming a live time of 1000 days [START_REF] Aprile | Double-weak decays of 124 Xe and 136 Xe in the XENON1T and XENONnT experiments[END_REF]. The contents and the details of this analysis will be presented in this chapter.

For its comprehension, the reader's attention must be pointed toward the particular context in which those analyses were performed. While the final results are presented in a joint paper, the timeline of each analysis was not the same. Several choices along the analysis process were made to ensure consistency among them, especially regarding the 0νββ decay projection study of XENONnT presented in the following. Those choices will be explicitly indicated and discussed in their relevant sections.

The study of double-weak decays, such as the 0νββ decay of 136 Xe, and the standard search of WIMP Dark Matter for which the XENON experiments were originally designed, is quite different from several points of view summarized in table 5.1. In contrast to the usual search of NR from WIMP-Nucleus elastic scattering performed at low energy, i.e., at the O(keV) scale, the analysis discussed in this work needs to be developed at the O(MeV) energy scale. The feasibility of such analysis, which strongly relies on the signal reconstruction's accuracy, has already been demonstrated in XENON1T [START_REF] Aprile | Energy resolution and linearity of XENON1T in the MeV energy range[END_REF] with several improvements in treating high-energy signals 2 . The development of those improvements was conducted prior to the analysis discussed in this work and fits perfectly in its scope. Therefore, a mention of the critical corrections and optimizations impacting the 0νββ decay search will benefit the reader, who can eventually look for a more detailed description in the following references [START_REF] Aprile | Energy resolution and linearity of XENON1T in the MeV energy range[END_REF][START_REF] Capelli | Search for Dark Matter and Neutrinoless Double Beta Decay in XENON1T and Calibration of the Photosensors in XENONnT[END_REF][START_REF] Wittweg | Second-Order Weak Decays in XENON1T and Future Xenon Time Projection Chambers[END_REF][START_REF] Therreau | Analyse de données de l'expérience XENON1T: Calibration des reculs électroniques pour des énergies comprises entre quelques keV et 3 MeV[END_REF].

One of the primary concerns when dealing with high energy signals is the saturation effect from PMTs. In XENON1T, all the channels are amplified 3 by a factor of 10 to improve the photo-detection efficiency, which is a crucial factor in probing lower-mass DM candidates that would result in a smaller nuclear recoil, and thus smaller S1 and S2 signals. The side-effect of this necessary amplification is the saturation of the 2.25

V ADC dynamic range that starts to appear for S2s induced by an energy deposition of O(100 keV) and becomes more relevant at higher energies where even the PMTs themselves can saturate. This effect leads to a loss of information on the number of incident photons.

Since S1 signals do not undertake gas amplification and are more evenly distributed beetween the two PMT arrays, saturation is not expected for them. Both position and energy reconstruction are affected by this saturation effect. Based on the signal measured by non-saturated PMTs far from the x-y interaction position, a correction is used in XENON1T and XENONnT on S2 signals [START_REF] Aprile | Energy resolution and linearity of XENON1T in the MeV energy range[END_REF]. Furthermore, to even further reduce the saturation effect of those PMTs at high energy, XENONnT sensors are read out with an amplification factor of ×0.5, in addition to the ×10 amplification used for DM searches.

Secondary signals induced by the primary S1 and S2 signals, such as afterpulses (AP) and secondary electrons (SE) already discussed in section 4.2.1, can lead to an overstimation of the reconstructed energy if they are not properly separated from the primaries.

This effect is accentuated at high energy as the magnitude, and temporal width of the S2s signals increase the number of secondaries and the difficulty of separating them from the primaries. Two complementary peak clustering and splitting algorithms were developed 2 MeV energies are considered high energies compared to the standard DM search (to reformulate). 3 The DAQ system is discussed in section 3.3.5.

to improve the separation of secondaries from the primaries and the distinction between multiple primaries. Improvements in the separation of secondary signals in addition to the PMTs saturation correction resulted in the linearity of the S1 and S2 signal's dependence on the deposited energy up to 2.6 MeV, allowing XENON1T to reach the best energy resolution at the Q ββ ever achieved so far in xenon TPCs [START_REF] Aprile | Energy resolution and linearity of XENON1T in the MeV energy range[END_REF]. The reconstructed energy spectra, energy resolution (σ/µ), and deviation of the reconstructed energies E r from the true peak energies E t for both SS and MS data are shown in figure 5.1 and include the high-energy enhancements mentioned previously in the XENON1T analysis framework. The observed energy resolution at the Q ββ of 136 Xe is 0.81% improving the previous values from dual-phase xenon TPCs such as LUX [START_REF] Akerib | Signal yields, energy resolution, and recombination fluctuations in liquid xenon[END_REF] or PandaX-II [START_REF] Ni | Searching for neutrino-less double beta decay of 136 Xe with PandaX-II liquid xenon detector[END_REF].

This promising result opens the path to the development of a dedicated 0νββ decay search using a dual phase liquid xenon detector and motivates the interest in performig a sensitivity study of the 0νββ decay in XENONnT. This analysis is based on MC simulations and a careful study of all the background sources. The identification and study of background sources represents one of my main contributions to this analysis.

Monte Carlo simulation framework

Signal and background models for the XENONnT 0νββ decay search projection study are derived from MC simulations performed in a framework developed by the XENON collaboration and based on the GEANT4 (GEometry And Tracking) toolkit version v.10.3.3 [START_REF] Agostinelli | Geant4a simulation toolkit[END_REF]. The geometry and materials composition of the detector are virtually built in GEANT4, that also handles the simulation of physical processes induced by the interaction of particles. To build a realistic model from the MC simulation, it is necessary to have sufficiently large statistics to reproduce (or exceed) the expected exposure during the lifetime of the expriment. XENONnT is expected to operate for at least five years.

It corresponds to a requirement of O(10 9 ) events from the materials and O(10 8 ) from intrinsic backgrounds. Generating this order of magnitude of events using MC simulations requires a strong requirement in terms of computational power, that can be reached thanks to use of the Open Science Grid (OSG) [START_REF] Pordes | The open science grid[END_REF][START_REF] Sfiligoi | The pilot way to grid resources using glideinwms[END_REF] platform that gives access to an extensive resource of CPU time. The workflow of the MC framework used in this study consists in the following successive steps:

1. A background source of interest is simulated with GEANT4. The position, time, deposited energy, particle type, and process responsible for each energy deposition in the sensitive LXe volume per simulated events are recorded and saved in Raw-G4

files based on the ROOT data format [START_REF] Brun | ROOT an object oriented data analysis framework[END_REF].

2. Those Raw-G4 files are then processed with the nSort tool, developed by the XENON collaboration, whose primary purpose is to cluster the energy depositions in each event according to the detector spatial resolution and separation power. The processed events are then saved in nSort-G4 ROOT files.

3. Merging of all the nSort-G4 processed files produced by the multiple parallel jobs into a single Isotope-Volume-processed ROOT file for the studied volume and isotope.

4. Application of different selection criteria to the Isotope-Volume-processed file in order to derive the energy spectrum for signal-like events.

5. Smearing of the energy spectrum to account for the energy resolution of the detector.

6. Normalization of the smeared energy spectrum to convert the number of count to an event rate which corresponds to our signal or background model.

Detector effects

While GEANT4 is used to reproduce the physical processes occurring in the experiment, it is necessary to consider the different detector effects that can affect the measured S1 and S2 signals with respect to the truly produced quanta of light and charge. The main properties we want to reconstruct from the MC simulation and use in this study are the energy deposition, the position, and the multiplicity of an event. In the following, we will detail how the relevant detector effects are modeled and applied to the MC simulation leading to a realistic simulation of the energy spectra.

Spatial and Separation Resolution

The multiplicity of an event, i.e., the number of interaction vertices the detector can discriminate, depends on its position resolution and separation power. This characteristic allows for identifying Single Scatter (or Single-Site, SS) and Multiple Scatter (or Multi-Site, MS) events and, similarly to the WIMP search, can be used to discriminate between 0νββ decay and backgrounds events, as it will be discussed in section 5.2. The separation power of the detector is mostly driven by its capacity to distinguish and split S2s originating from interaction vertices at different depths. Indeed, as illustrated in Figure 5.2, in the case of an event with two intereactions A and B, at a different depth (∆Z) in the TPC, the two electron clouds produced at each vertex will drift towards the gas phase and produce S2s that can be merged, this is the case for example of pile-up S2s that are too close in time to be separated one from each other. The minimal ∆Z required to distinguish the two electron clouds depends on the deposited energy in each vertex, leading to different sizes of electron clouds impacting the S2s width and the relative depth of both In XENON1T, the modeling of the separation power is based on MC simulation carried out with PAX, the waveform simulator framework. Various configurations of MS events were produced for different S2s areas, separation, and position of interactions in outputs and a solid red line once the energy resolution of the detector is applied. We can see that the gamma peaks are properly smeared out accordingly to the energy resolution at their corresponding energy given by equation 5.1.

σ (E) µ (E) = a √ E + b (5.1)

Rate conversion of MC Simulation

In order to give a meaningful interpretation to the result of the MC simulation, it is necessary to convert the number of generated events satisfying a set of selection criteria (that will be introduced in the next section) into a realistic rate of events expected in the detector. The ER background rate R i,j , for a specific radioactive isotope i and component j, is then defined as:

R i,j = N cut i,j T eff i,j × M FV × ∆E (5.2)
Where N cut i,j is the number of events surviving the selection criteria, M FV is the mass of the fiducial volume considered in this analysis, ∆E is the size of the energy binning used to produce the energy spectrum (1 keV in this work), and T eff i,j the effective livetime of the simulation, i.e., the equivalent livetime necessary for the experiments to cumulate a similar statistics. It is defined as:

T eff i,j = N G i,j W i × M j × A i,j (5.3)
With N G i,j the number of generated events in GEANT4 for the isotope i in the component j, M j the mass of the component j, A i,j the specific activity in µBq/kg of the isotope i in the component j. Due to a particular feature in our GEANT4 framework, we had to implement a weighting factor W i to consider that for a given isotope part of a decay chain, one event in GEANT4 does not correspond to the full decay chain. Instead, each step of the chain is split in a different event. We thus consider the mean decay chain length for each studied isotope i as the value for W i . The latter term is most relevant in the case of materials background study that will be discussed in more detail in section 5.3.

In this work, the selection criteria that we will consider in order to select events mimicking the signature of our signal are:

• Multiplicity cut: As it will be introduced in section 5.2, the signature of a 0νββ decay is expected to be a Single-Site interaction. Therefore all Multi-Site interactions from background sources will be rejected.

Two different types of background sources can mimic this signal signature in our detector: external and internal sources, whose study will be the object of the next two sections.

Materials background

The detector materials used to build the different elements of the experiment, described in chapter 3, were carefully chosen based on their radiopurity to minimize the induced background for the WIMP search as much as possible. Nevertheless, even at the trace level, they still contain long-lived radionuclides such as the natural decay chains of 238 U, 235 U, and 232 Th, shown in figure 5.6, can introduce ER background. In particular, the 214 Bi and 208 Tl γ-lines ( 238 U and 232 Th daughters) at 2447.9 keV and 2614.5 keV, respectively, are close to the Q ββ , and their interaction in LXe can mimic the signature of 0νββ decay.

Another source of background relevant to our study is represented by the decay of 60 Co in two γ-lines at 1173.2 keV and 1332.5 keV, respectively. Being not temporarily resolvable, the two peaks could pileup and be reconstructed as a unique peak at 2505.7 keV close to the Q ββ .

The material backgrounds were already studied at low energy in the XENONnT WIMP projection study [START_REF] Aprile | Projected WIMP sensitivity of the XENONnT dark matter experiment[END_REF], using a detailed MC simulation. This work will benefit from the existing MC simulation sample to model the material background relevant for the 0νββ decay search. A dedicated screening campaign7 has been carried out on [START_REF] Aprile | Material radiopurity control in the XENONnT experiment[END_REF] to measure the specific activity of a given isotope for materials used to build the different components of the detector.

The results of the screening measurements are summarized in table 5.2, for the different isotopes of interest for the 0νββ decay search mentioned above, but also for isotopes of interest for the WIMP search, such as 137 Cs (β-decay with an end point at 512 keV) and 40 K (β-decay with an end point at 1.3 MeV). Furthermore, the 238 U and 232 Th decay chains 8 were split into an early and late part, as described in equation 5.4, to account for the non-secular equilibrium induced by the presence of long-lived daughter nuclei as indicated in figure 5.6. Table 5.2: Material contamination from screening campaign given in µBq/kg [START_REF] Aprile | Material radiopurity control in the XENONnT experiment[END_REF]. For the PMTs the contamination level is given in µBq/PMT. The reported contamination for the PMTs is the average contamination of the XENON1T re-used PMTs and the new ones. Upper limits are given if no activity above background was found, in this case, for a conservative approach, these upper limits are considered as a central value with no uncertainty. Components/isotopes whose contamination was not available are excluded from the analysis. For consistency with the XENON1T 0νββ decay data analysis, we scaled the screened activity of all the components for those two isotopes up to May 1 st , 2020. The correction of the 60 Co activity, A c (t), follows the radioactive decay law equation:

A c (t) = A screening • e - ln(2) • t T 1/2 (5.5)
With A screening , the measured activity during the screening campaign, T 1/2 the 60 Co half-life, and t the time difference between the screening date and the 1 st of May 2020.

The case of 228 Th needs a different treatment since we are in the case of a decay chain that can be simplified to the following form when short-lived daughter nuclei are omitted:

232 Th → 228 Th → 224 Ra. We used the Bateman equation as a mathematical model to describe the evolution of the 232 Th (Parent nuclei, identified as 1) and 228 Th (Daughter nuclei, identified as 2), which are driven by the following differential equation:

dN 2 (t) dt = -λ 2 N 2 (t) + λ 1 N 1 (t) (5.6)
Whose solution can be written as:

A 2 (t) = λ 2 N 2 (t) = λ 2 N 2 (0) exp (-λ 2 t) -N 1 (0) λ 1 λ 2 λ 2 -λ 1 [exp (-λ 2 t) -exp (-λ 1 t)] = A 2 (0) exp (-λ 2 t) -A 1 (0) λ 2 λ 2 -λ 1 [exp (-λ 2 t) -exp (-λ 1 t)]
(5.7)

Where A i (0) is the specific activity at the time of the screening measurements, λ i is the decay constant, t is the time difference between the screening date and the 1 st of May 2020, and A 2 (t) is the corrected activity for 228 Th.

In addition to the specific activity A i,j of the different isotopes i and components j simulated and their masses M j , the last ingredients needed to compute the effective livetime T eff i,j , of a given simulation is the weighting factor, W i , as introduced in section 5.1.3. This parameter was estimated for each isotope using simulated events fully contained in the LXe sensitive volume 9 and computing the mean number of steps for each decay chain: results are summarized in table 5.3. We can now normalize all the simulated events, from material MC simulations to a rate of events/year using the effective livetime T eff i,j determined using the different inputs presented above. This method allows us to exploit the MC simulation to define an optimal FV for 0νββ decay search with XENONnT.

Table 5.3: Summary of the weighting factor used to take into account the decay chain splitting in G4. Each value corresponds to the mean number of steps in the corresponding isotope decay chains. Some isotopes shows rather large uncrtainty, due to the presence of non-negligible branching ratio in the decay chain that leads to different final numbers of steps.

Isotopes

Fiducial volume optimization

The primary source of background at MeV energies is due to γ-rays from detector materials reaching the LXe active volume. It is, therefore, necessary to define an optimal FV that can efficiently suppress this external source of background while maximizing the target mass. As shown in equation 2.40, those two parameters strongly impact the expected sensitivity for 0νββ decay. The optimization of the FV shape follows the same procedure used for the XENON1T 0νββ decay data analysis and was carried out in collaboration with A. Rocchetti. It start with the definition of a figure of merit (FoM) proportional to the sensitivity:

FoM = M FV √ R b (5.8)
Where M FV is the total LXe mass in kg and R b is the total background rate (in events/yr) expected within a given FV. The sensitive xenon volume was segmented into 64 bins with (8 × 8) equal bins in the (z, R 2 ) parameter space 10 . The sensitivity figure of merit FoM i , as defined in equation 5.8, was calculated for each bin of index i, using events within 2σ E energy-resolution windows at Q ββ . The FoM values are then smoothed to 100 contour levels. The result is shown in figure 5.8 where 25 contours have been considered to test the optimal FV are shown. The contours are shifted towards the bottom of the TPC due to the reduced shielding power of the GXe phase and the larger mass of materials at the top of the detector. Those contours are then fitted with a pair of two semi-superellipsoids with opposite curvature, one for each upper and lower part of the TPC. Using two different and independently optimized functions allows one to define asymmetric FV shape to expand the volume as much as possible. The superellipsoids are defined as:

Internal background

In addition to the external sources of backgrounds discussed previously, the second category of backgrounds we must investigate are the internals. They are either intrinsic to the xenon target itself, i.e., contamination from radionuclides, or originate from interactions of cosmogenic particles with the xenon target. Therefore, they are expected to be homogeneously distributed in the whole LXe target. The purpose of this section is to study the different internal background sources to the 0νββ search in XENONnT listed below:

• Radiogenic and cosmogenic production of the 137 Xe β-emitter.

• β-γ-decay from 214 Bi induced by 222 Rn emanation.

• Two neutrino double beta decay of 136 Xe.

• 8 B solar neutrino-electron scattering.

While we expect the internal backgrounds to be sub-dominant compared to the one from the materials, as shown in figure 5.4, it is necessary to study them to improve our understanding of those backgrounds that might be relevant or dominant for the future generation of xenon dual-phase TPC aiming to look for 0νββ decay search, such as DAR-WIN [START_REF] Agostini | Sensitivity of the DARWIN observatory to the neutrinoless double beta decay of 136 Xe[END_REF].

Radiogenic and cosmogenic production of the 137 Xe β-emitter

The β-decay of 137 Xe illustrated in figure 5.11, with a Q-value at 4173.7 keV far beyond the Q ββ and a half-life of 3.82 min, is a relevant source of ER background for 0νββ decay search. 137 Xe is produced through neutron capture on 136 Xe occurring either within the TPC itself or in the non-shielded parts (outside of the water tank) like the purification systems. The daughter nucleus induced by the neutron capture process is usually in an excited state and will relax to the ground state immediately with the emissions of several γ-rays. These gammas could be tagged and thus rejected, at the price of a loss of exposure that needs to be studied.

Neutron sources

The first and more challenging step is to estimate the production rate of 137 Xe through neutrons capture on 136 Xe in XENONnT. We can identify four relevant origins of neutrons, illustrated in figure 5.12 and listed in the following, that could contribute to the 137 Xe production.

• Neutrons from natural radioactivity in the cavern: these neutrons come from (α,n) reactions from the U and Th decay chain and spontaneous fission of respect to the material backgrounds. Instead, a more conservative approach was used to set an upper limit on the production rate of the 137 Xe in the purification systems.

The modelization of the 137 Xe production in the purification loop is based on an analytical approach. As it is illustrated in figure 5.15, we will consider that all elements of the purification system are in parallel: even if we are aware that this is just an approximation and not completely accurate (there are some internal loops among the considered elements), in first approximation this assumption is realistic. Additionally, we decided to not take into account for the possible shielding effects of the purification loop materials:

this choice appears to be quite conservative, leading to an overestimation of the neutron flux reaching the xenon detector volume. Furthermore, in order to evaluate the upper limit of the 137 Xe production in the purification loop, we decided to neglect the impact of other xenon isotopes present in the natural xenon. The analytical model used to estimate the amount of 137 Xe produced and flowing back into to the TPC is the following:

A P U R i =   Φ • σ n-capt • η 136 Xe • N m • α t M tot LXe   • i m i • e -t i • ln 2 T 1/2
(5.10)

With φ = (1.00 ± 0.67) × 10 -6 cm -2 s -1 the mean thermal neutron flux measurements made at LNGS, σ n-capt = (0.238±0.019)×10 -24 cm 2 the neutron capture cross-section for 136 Xe from [START_REF] Albert | Measurement of neutron capture on 136 Xe[END_REF], m i and t i the mass and average travel time of LXe in each sub-system i, M tot LXe = 8326 kg the total mass of LXe, and α t a conversion factor from seconds to years. Finally, η 136 Xe = (8.86 ± 0.54) % is the natural abundance of 136 Xe 11 , N m = 4.6 • 10 24 the amount of Xe nuclei per kg, and T 1/2 = 3.82 min the 137 Xe half-life. We can distinguish two terms, also illustrated in figure 5.15: one corresponding to the production of 137 Xe and another one that accounts for the decay probability of the 137 Xe prior to entering back into the TPC (due to the short half-life of 137 Xe).

For the sake of clarity, the decay term of the expression will be referred to as B i in the following work.

B i = i m i • e -t i • ln 2 T 1/2 ; i ∈ [LXe ; GXe ; Rn]
(5.11)

The uncertainty on the 137 Xe production rate in the purification loop from equation 5.10, assuming the quantities Φ, σ n-capt , η 136 Xe , and B i , is given by:

∆A P U R i A P U R i = ∆Φ Φ 2 + ∆σ n-capt σ n-capt 2 + ∆η 136 Xe η 136 Xe 2 + ∆B i B i 2
(5.12) 11 Due to the addition of 5.7 t of xenon to the total inventory of XENON1T, we conservatively assumed a natural abundance of 136 Xe in xenon, using the difference with respect to the XENON1T measured abundance of η 136 Xe = (8.49 ± 0.04 stat ± 0.13 sys ) % as a systematic uncertainty.

LXe loop

GXe loop

Rn Column

Water Tank TPC n 137 Xe produced through (n,ɣ) process on Xe136

A PUR i = ( Φ ⋅ σ n-capt ⋅ η ⋅ N m ⋅ α t M tot LXe ) ⋅ [ ∑ i m i ⋅ e -t i ⋅ ln 2 T 1/2
] Production Decay Fig. 5.15 -Simplistic illustration of the xenon circulation between the TPC (shielded by the WT) and the three purifiation systems considered in parallel in a non-shielded environment. The production of 137 Xe in the purification systems (green square) is illustrated with red dot. The diminishing number of dots from the purification system up to the TPC (in the orange squares), illustrates the decreasing rate of 137 Xe before reaching the TPC.

Where the uncertainty on B i can be calculated using the formula:

f (x 1 , x 2 , ..., x i ) -→ ∆f = i ∂f ∂x i 2 ∆x 2 i (5.13)
Which leads to the following expression:

∆B 2 i = e -t LXe • ln 2 T 1/2 2 • ∆m 2 LXe + - ln 2 T 1/2 • e -t LXe • ln 2 T 1/2 2 • ∆t 2 LXe + e -t GXe • ln 2 T 1/2 2 • ∆m 2 GXe + - ln 2 T 1/2 • e -t GXe • ln 2 T 1/2 2 • ∆t 2 GXe + e -t Rn • ln 2 T 1/2 2 • ∆m 2 Rn + - ln 2 T 1/2 • e -t Rn • ln 2 T 1/2 2 • ∆t 2 Rn (5.14)
Using all those information, we estimated the production rate of 137 Xe in the purification system, entering back into the TPC. Results are summarized in table 5.4 together with the mass and average travel time of xenon in each sub-system. As a conservative choice, we did not consider the migration time from the outer LXe shell to the inner volume, which would further reduce the impact of 137 Xe from the purification loop. However, we considered the traveling time necessary for the xenon in the pipes from each reduce the statistical uncertainty, a larger sample of events was necessary to have a sufficiently large number of γ reaching the FV. The mass of xenon in the LXe shell geometry is M Shell = 2455 kg.

In both cases, we only simulated the part of the decay chain of interest for 0νββ decay, i.e., 214 Bi → 214 Po, leading to a weighting factor W i value of 1 for the normalization of the rate. In this study, we assumed the XENONnT baseline 222 Rn contamination expected to be A 214 Bi = 1.0 ± 0.1 µBq/kg of xenon. However, the daughter nuclei of the 222 Rn decay chain have already shown in the previous generation of xenon experiments to not exhibit the same contamination level as we could expect. This is due to ionized 222 Rn daughter nuclei that get trapped by the cathode or the PTFE wall of the TPC when drifting or through natural convection of the LXe. The observed ratio between 222 Rn α-decay and BiPo events is κ Rn/BiPo = 54.3% as measured in XENON10014 [START_REF] Aprile | Intrinsic backgrounds from Rn and Kr in the XENON100 experiment[END_REF]. The contamination level that will be used to normalize the energy spectrum, in both cases with their corresponding masses mentioned above, as described in section 5.1.3 are the following:

A AV 214 Bi = (1 -ϵ BiPo ) • κ Rn/BiPo • A 214 Bi A Shell 214 Bi = κ Rn/BiPo • A 214 Bi
(5.15)

Figure 5.17 shows the energy spectra for both components of the 214 Bi backgrounds.

The associated uncertainties are 10% and 50% near the Q ββ for the active volume and LXe Shell component, respectively. The main source of uncertainty for the AV spectrum is due to the error associated to A 214 Bi , while the LXe Shell spectrum is dominated by statistical uncertainty. Both components will be implemented separately to the XENONnT background model for the 0νββ decay search.

2νββ of 136 Xe

The 2νββ of 136 Xe is a natural background for the search of 0νββ , this rare double weak decay has been introduced in section 2.1.3.1. In order to model properly the expected energy spectrum induced by such a process, different options are available:

• Analytical approach: A standard approximation used to describe the 2νββ spectral shape is the Primakoff-Rosen (PR) approximation [START_REF] Boehm | Physics of Massive Neutrinos[END_REF], which is based on the simplified non-relativistic Coulomb expression [START_REF] Primakoff | Double beta decay[END_REF]. In this approximation, the summed electron energy spectrum follows the form of equation 5. [START_REF] Dolinski | Neutrinoless double-beta decay: Status and prospects[END_REF], where T corresponds to the summed kinetic energies of the two electrons and Q to the total parameters were let free during the fit that leads to the following value: b = 2.25 ± 0.5 and c = (6.5 ± 2.1) × 10 3 . We can directly use this function to implement the detector's spatial resolution and separation power to the theoretical spectrum.

To estimate the total uncertainty on the expected background rate from 136 Xe 2νββ decay properly, several aspects must be considered since some uncertainty are constant over the whole energy spectrum, while others are energy dependent. The total relative uncertainty considered in first approximation in this work is given by:

∆R i R i = ∆S Xe136 S Xe136 2 +
+   ∆T Xe136 1/2 T Xe136 1/2   2 (5.20)
The second and third terms correspond to the uncertainties from the detector effects, derived based on the largest relative difference between the final energy spectra obtained using the different combinations of parameters for the energy resolution and SS proportion function within their error range. In the case of the energy smearing, the uncertainty is energy dependent but is at the sub-percent level and therefore considered negligible in this work.

The fourth term is a systematic uncertainty added to take into account the shape difference between the HSD and SSD theoretical spectra from Kotiala-Iachello [START_REF] Kotila | Phase-space factors for double-β decay[END_REF]249],

discussed in section 2.1.3.1, and shown in figure 5.20. Both spectra exhibit a larger relative difference at low energy, which is the ROI for WIMP search, and at high energy near the Q ββ , which is the ROI for 0νββ decay search. The maximal value of the relative difference between the two spectra in the 0νββ decay ROI is 17.5%. However, since the 2νββ spectra will be dominant a lower energy, where the difference between the two approach is negligible, this term will not be used in the final calculation.

The last term comes from the uncertainty on the computation of the PSF, as listed in table VI of KI paper [START_REF] Kotila | Phase-space factors for double-β decay[END_REF]. We need to account also for uncertainties related to the Q ββ , the nuclear radius (∆ Radius = 0.5 %), and screening effects (∆ Screening = 0.1 %), which are again summed quadratically:

Inference

The inference framework presented in this section has been build by T. Wolf. To derive the expected sensitivity for 0νββ decay search in XENONnT, a Poisson binned log-likelihood ratio where nuisance parameters are profiled [START_REF] Cowan | Asymptotic formulae for likelihood-based tests of new physics[END_REF], was used to constrain the observable rate of 0νββ decay events, noted A 0νββ , and convert it into half-life. The 0νββ decay signal is modeled as a Gaussian peak at µ 0νββ = 2457.8 keV and a width σ 0νββ = 19.7 keV as shown in section 5.2. The binning is performed in the energy parameter space with a bin size of 1 keV. The Poisson likelihood L reads:

L A 0νββ , ⃗ θ = bins i Poisson N i , λ i ( ⃗ θ) + N s i (A 0νββ , ⃗ θ) × constraints j Gauss (θ j , µ j , σ j ) (5.24)
Where N i is the measured number of events in each energy bin, λ i is the number of expected background events as a function of the nuisance parameters ⃗ θ. The number of expected signal events in bin i is denoted with N s i and depends on the signal strength A 0νββ and the nuisance parameters ⃗ θ. Each constrained nuisance parameter θ j , listed in table 5.5, has an expected mean value µ j with a standard deviation σ j , obtained from dedicated MC study that were presented in section 5.3 and 5.4 (background models and their corresponding uncertainties). The log-likelihood ratio (LLR) test statistic used is defined as:

-2LLR = -2 ln L A 0νββ , ⃗ θ L Â0νββ , ⃗ θ (5.25)
Where quantities with a single hat denote the set of parameters corresponding to the unconditional maximum of the likelihood while quantities with two hats denote the set of parameters maximizing the conditional likelihood. The allowed range of A 0νββ were constrained to be positive.

To determine the sensitivity, we perform likelihood scans on an Asimov dataset 16testing the amplitude of the signal peak, A 0νββ , for a set of assumed livetimes of the experiment (between 10 days and 1000 days), as shown in figure 5.25. The red line denotes the threshold stemming from the 90% quantile of a χ 2 distribution with one degree of freedom [START_REF] Baker | Clarification of the use of chi-square and likelihood functions in fits to histograms[END_REF].

background source suffers from a rather larger uncertainty, as shown in table 5.5, due to the uncertainties in the screening measurements. Therefore, new materials must be considered to reduce the impact of the materials backgrounds for the next generation of xenon dual-phase TPC while remaining competitive with experiments dedicated to 0νββ decay search. It is the case of DARWIN that investigates its sensitivity to 0νββ decay search with a titanium cryostat. Using a copper cryostat would be a must, but imply a drastic change in cryostat technology (currently double-walled cryostat with vacuum isolation), which is not straightforward. Furthermore, the sensitivity to 0νββ decay search would benefit from a more stringent constraint of the materials backgrounds. This would require an improvement in the precision of screening measurement technics.

The study of internal sources of backgrounds for 0νββ decay search is also primordial for the next generation experiment that aims to be dominated by them. Among those studied in this chapter, the 137 Xe background has shown a particularity that must be considered in future experiments: its production in non-shielded environments outside the water tank. Indeed, while the size of the detector, and thus its xenon target, increase at each new generation of experiments, it is also the case for the amount of xenon that circulates outside of the water tank in order to be purified and cooled down. Thus, the production of 137 Xe in a non-shielded environment will also scale with the size of the experiments and potentially limit their sensitivity to 0νββ decay search. Nevertheless, this contribution can be efficiently mitigated by shielding the main purifications and cryogenics sub-systems (with materials enriched in H to suppress the thermal neutron flux).

Conclusion

This work investigates the expected sensitivity of the XENONnT experiment for the neutrinoless double beta decay search of 136 Xe. A projection study, based on Monte Carlo simulation derived from a detailed estimation of both backgrounds and signal models, has been carried on. This results in a lower limit on the half-life of the process of • Les bruits de fond externes sont principalement originaires de la radioactivité naturelle des matériaux utilisés pour construire l'expérience, ou présents dans son environnement (roches et béton). Cette radioactivité naturelle est une source de neutrons, γ, β, et α qui peuvent atteindre le volume de détection de l'expérience.

T 0νββ 1/2 > 2.1× 10
Afin de se prémunir contre ce type de bruits de fond, la sélection des matériaux utilisés pour construire l'expérience fait l'objet d'une campagne de mesures intensives afin de minimiser la contamination d'éléments radioactifs. De plus, il est commun d'utiliser plusieurs couches de blindages successifs afin de protéger le détecteur de la radioactivité environnementale. Ces systèmes de blindages peuvent être passifs ou actifs offrant ainsi une capacité d'identification et de rejet de certains bruits de fond.

• Les bruits de fond internes dus aux isotopes radioactifs intrinsèques aux milieux de détection. Ils sont naturellement présents, introduits par l'émanation des matériaux, ou produits par activation via les particules (neutrons ou muons) induits par les deux autres types de bruits de fond mentionnés précédemment. La purification, lorsqu'elle est possible, de la cible et du milieu de détection permet d'atténuer le niveau de contamination interne des expériences à bas bruit de fond.

Pour certains types de détecteurs, des techniques de discrimination pour certains types d'interaction permettent de réduire encore davantage ces sources de bruit de fond.

Les expériences de physique d'événements rares peuvent mettre en oeuvre une large gamme de techniques de réduction du bruit de fond afin de maximiser leur sensibilité.

Tandis que les familles de bruits de fond mentionnées ci-dessus sont communes à toutes les expériences de physique d'événements rares, la nature précise des bruits de fond (iso- ) mais pas sur la valeur absolue de ces masses. Une mesure de la valeur absolue des états de masses des neutrinos reste néanmoins possible, mais requiert de faire appel à deux autres types d'approches. La mesure directe via l'étude précise d'un spectre-β, ou une mesure indirecte notamment via l'observation d'un processus extrêmement rare et encore inobservé à ce jour : la désintégration double bêta sans émission de neutrinos (0νββ ). Cette seconde approche permet également de déterminer la nature des neutrinos, à savoir s'ils sont des particules de Dirac ou de Majorana3 et d'élucider la question de l'origine de la masse des neutrinos. En effet, alors que l'observation de l'oscillation des neutrinos a permis de démontrer que les neutrinos ont une masse non nulle, cette même masse doit être extrêmement faible (< 1 eV) pour ne pas avoir été mesurée jusqu'à présent, notamment par les expériences de détection directe. L'ordre de grandeur de la masse des neutrinos est bien plus faible que pour les autres fermions (> 6 ordres de grandeur), ce qui est difficilement explicable dans le cadre du MS. La question se pose donc de savoir si la masse des neutrinos est générée par le même mécanisme que les autres fermions, ou si elle est générée par un mécanisme différent.

Trois mécanismes sont envisagés pour expliquer l'origine de la masse des neutrinos :

• Mécanisme de Dirac : Cette approche suppose que les neutrinos sont des particules de Dirac et acquièrent leurs masses de la même manière que les autres fermions, à savoir via l'interaction avec le champ de Higgs. Ce mécanisme implique l'existence de neutrinos qui n'interagissent pas via l'interaction faible mais uniquement par la force gravitationnelle, appelés neutrinos stériles (en opposition avec les neutrinos actifs). Ces neutrinos stériles n'ont pas encore été observés, mais sont recherchés dans de nombreuses expériences.

• Mécanisme de Majorana : Une autre alternative pour expliquer l'origine de la masse des neutrinos est de supposer que les neutrinos sont des particules de Majorana (les neutrinos sont leurs propres antiparticules) et obtiennent leurs masses via un mécanisme différent des autres fermions. Cependant, ce mécanisme met en jeu une nouvelle physique au-delà du MS car il implique une non-conservation du nombre leptonique. L'une des grandes implications de ce mécanisme est la possibilité d'expliquer l'asymétrie matière-antimatière observée dans notre Univers.

• Mécanisme de la balançoire : La dernière approche, la plus populaire au sein de la communauté scientifique, prend en compte les deux termes de masses de Dirac et Majorana tout en supposant que les neutrinos sont des particules de Majorana et permet d'expliquer l'ordre de grandeur très faible de la masse des neutrinos actifs via l'existence de neutrinos stériles beaucoup plus lourds (analogie de la balançoire).

La détermination de la nature du neutrino, Majorana ou Dirac, est donc une question fondamentale de la physique des particules. L'une des meilleures pistes pour répondre à cette question consiste à rechercher un processus ne respectant pas la conservation du nombre leptonique, tel que la désintégration 0νββ qui fait l'objet principal de cette thèse dans le cadre de l'expérience XENONnT.

La désintégration double beta sans émission de neutrino est un mode particulier de désintégration doublement faible, processus du second ordre de l'interaction faible extrêmement rare correspondant à une transition nucléaire isobarique partant d'un noyau père doublement pair (A, Z) vers un noyau fils (A, Z ± 2) via la conversion simultanée de deux nucléons. Différents modes de désintégration doublement faible autorisés par le MS ont été théorisés et observés expérimentalement pour 12 noyaux différents jusqu'à présent. L'ordre de grandeur des demi-vies mesurées pour ces processus varie de 10 19 à 10 24 années, correspondant en effet à des processus extrêmement rares. En complément de ces désintégrations doublement faibles autorisées par le MS, un second mode de désintégration peut être envisagé pour chaque processus, si l'on considère que les neutrinos sont de Majorana, n'impliquant pas l'émission de neutrinos. L'exemple de la désintégration double-β -avec et sans émission de neutrino4 est donné dans l'équation A.1.

2νβ -β -: (A, Z) → (A, Z + 2) + 2e -+ 2ν e 0νβ -β -: (A, Z) → (A, Z + 2) + 2e - (A.

L'objectif de cette thèse est de déterminer la sensibilité de l'expérience

XENONnT pour la recherche de la désintégration 0νββ de l'isotope 136 Xe. Sachant que cette expérience a pour but principal la détection directe de matière noire et a été optimisée pour cette recherche qui, comme nous allons le voir dans la suite, implique la création de signaux bien différents, que ce soit en termes d'énergie ou de type d'interaction, que ceux attendus dans le cas de la désintégration 0νββ .

Le concept de Matière Noire (MN), tel qu'il est compris aujourd'hui, a vu le jour au début du 20 eme siècle à la suite de nombreuses observations astrophysiques soutenant l'hypothèse de l'existence d'une matière inconnue dans notre Univers. Ces observations, présentes à différentes échelles de l'Univers, indiquent que la masse visible de matière, c'est-à-dire la matière baryonique, ne suffit pas à expliquer les phénomènes observés. Afin La construction de XENONnT, qui a débuté en Mars 2019 en parallèle du désassemblage de XENON1T, avec la maintenance et l'amélioration de différents sous-systèmes s'est conclue par l'assemblage de la nouvelle TPC entre février et Mars 2020 et son transport jusqu'au laboratoire souterrain afin d'être insérée dans le cryostat en acier, marquant ainsi la fin de la phase de construction et le début de la phase de mise en service. Lors de cette phase, deux problèmes inattendus se sont produits. Premièrement, l'observation d'un court-circuit entre la cathode et l'électrode écran du bas qui fut observé lors de la montée en tension des électrodes vers leur valeur nominale (-30 kV pour la cathode).

Ce phénomène induisant une émission de lumière lorsque la tension est trop élevée, il a été décidé de limiter la tension de la cathode à -2.75 kV. Deuxièmement, un phénomène d'émission intense d'électrons à certaines positions de la phase gazeuse (x, y) a été observé lors de l'optimisation de la tension des électrodes responsables du champ d'extraction. d'étudier les effets de seuil en énergie.

• Source externe de 241 Suivi des rendements de lumière et de charge: Une autre des responsabilités principales endossées au cours de cette thèse, en lien avec l'exploitation des données du SR0 de XENONnT, a été le suivi de l'évolution des rendements (PE mesurés par keV d'énergie déposée) de lumière (LY) et de charge (CY) durant cette période. En tant que responsable de cette tâche qui incluait plusieurs analystes, j'ai dû coordonner les efforts de chacun afin de construire un cadre d'analyse officiel permettant la mesure et le suivi de ces paramètres. Le suivi du LY et du CY est un élément essentiel de l'analyse des données de XENONnT, car il permet de surveiller la stabilité du détecteur et de détecter les changements dans les conditions de fonctionnement. Le LY et CY sont mesurés à l'aide A.5. Estimation de la sensibilité de XENONnT pour la recherche de désintégration double beta sans émission de neutrino du 136 Xe de différentes sources (provenant de sessions de calibration ou naturellement présentes dans le détecteur) telles que les isotopes de 83m Kr, 129m Xe, 131m Xe, les α de 222 Rn et les γ de haute énergie provenant des matériaux, ont été utilisés. La variété de sources étudiées offre un suivi sur une large gamme d'énergie, allant de 9.4 keV jusqu'au MeV. Un exemple de mesure de ces rendements de lumière et de charge est décrit dans le corps principal du manuscrit pour le cas de 83m Kr. Cette étude a permis de démontrer une stabilité, des rendements de lumière et de charge sur la période de prise de données du SR0, avec une variation maximale inférieure à 1% pour le LY et 3% pour le CY.

Cette stabilité s'est maintenue, même pendant la période de collecte de données aveugles (post-juillet), où la variation du CY a diminué en dessous de 2%.

Il est nécessaire de spécifier que ce travail d'exploitation des données du SR0 de XENONnT a été réalisé dans le contexte des premières analyses de XENONnT qui étaient principalement orientées vers la recherche d'évènements rares à basse énergie, telle que la recherche de MN. Une extension de ces travaux afin de permettre des analyses à plus haute énergie, telle que pour la recherche de désintégration 0νββ , est nécessaire et sera entreprise une fois ces premiers résultats obtenus.

A.5. Estimation de la sensibilité de XENONnT pour la recherche de désintégration double beta sans émission de neutrino du 136 Xe L'étude principale de cette thèse, visant à estimer la sensibilité de l'expérience XENONnT pour la recherche de désintégration double beta sans émission de neutrino du 136 Xe, est présentée en détail dans le chapitre 5 de ce manuscrit. Ce travail a été réalisé dans le contexte plus général de l'étude, dans XENON1T et XENONnT, des désintégrations doublement faibles, telle que la désintégration 0νββ du 136 Xe. Les résultats de ce travail ont mené à une publication dans le journal Physical Review C dans laquelle je suis identifié comme l'un des auteurs principaux.

Comme cela a été énoncé plusieurs fois dans les sections précédentes, la recherche de désintégration 0νββ est bien différente de la recherche de matière noire pour laquelle l'expérience XENONnT a été optimisée. En effet, le type d'interaction (ER vs NR), la gamme en énergie (O(10) keV vs Q ββ ∽ 2457 keV ) et les sources de bruit de fond dominants (interne vs matériaux) sont différents. Cela nécessite un travail d'analyse des données dédié, qui au moment de la rédaction de cette thèse n'était pas encore achevé.

Néanmoins, une estimation de la sensibilité de XENONnT pour la recherche de désintégration 0νββ a pu être réalisée en utilisant des simulations Monte Carlo (MC). Dans cette section je vais présenter uniquement la structure générale de l'analyse, en insistant sur les points principaux auxquels j'ai contribué, avant de conclure en donnant les principaux résultats de cette recherche.

Outils de simulation Monte Carlo: Afin d'estimer la sensibilité d'une expérience d'évènements rares pour la recherche d'un processus physique particulier, il est nécessaire de savoir quel est le signal attendu et de déterminer les sources de bruits de fond qui lui seront associées. L'utilisation de simulation Monte Carlo est alors nécessaire afin de modéliser le signal et les bruits de fond, en tenant compte de la réponse du détecteur. Pour cette étude, la collaboration XENON a développé un outil de simulation MC basé sur GEANT4 (G4). Cet outil permet de modéliser la géométrie et la composition des matériaux du détecteur tout en gérant également la simulation des processus physiques induits par l'interaction des particules que l'on souhaite étudier. Pour construire un modèle réaliste à partir des simulations MC, il est nécessaire d'avoir une statistique suffisamment grande pour reproduire (ou dépasser) l'exposition attendue pendant la durée de vie de l'expérience. Cela peut représenter un défi pour certaines sources de bruit de fond, nécessitant des temps de calculs importants. Pour cette étude, les simulations MC ont été réalisées en utilisant les ressources de la plateforme de calcul partagée Open Science Grid. La modélisation du signal et des bruits de fond associés pour la recherche de désintégration 0νββ est un élément crucial de cette étude, dont j'ai été le responsable au cours de ma thèse. En utilisant les outils de simulations mentionnés précédemment, et via des études détaillées de chaque source potentiel de bruit de fond, j'ai pu déterminer une modélisation complète de chacun d'entre eux. Ces modèles étant des ingrédients essentiels pour déterminer la sensibilité de XENONnT pour ce processus rare. Une description de la modélisation du signal et de chaque source de bruit de fond est proposée ci-dessous.

• Signal: désintégration 0νββ du 136 Xe. Pour modéliser le signal attendu dans A.5. Estimation de la sensibilité de XENONnT pour la recherche de désintégration double beta sans émission de neutrino du 136 Xe XENONnT, des simulations MC ont été réalisées en utilisant le générateur d'événements DECAY0 qui fournit les propriétés (énergie et corrélation angulaire) des deux électrons émis lors de la désintégration. Ces informations sont ensuite utilisées dans G4 pour simuler l'interaction de ces électrons dans le xénon liquide. Les résultats de ces simulations démontrent que 91% des événements de désintégration 0νββ du 136 Xe sont des événements Single-Site (SS) dans le volume fiducial du détecteur. En effet, les électrons déposent leur énergie après quelques mm de xénon, il est donc peu probable de pouvoir les distinguer du fait du pouvoir de séparation du détecteur qui est de l'ordre du cm. Les simulations MC montrent que les événements reconstruits en tant qu'événements Multi-Site (MS) sont principalement dus à l'émission de photons de rayonnement de freinage par les électrons. Les deux électrons partagent une énergie totale fixe égale à la Q ββ de la désintégration, la forme du spectre attendu en tenant compte de la résolution en énergie du détecteur est un pic gaussien centré sur l'énergie. Le signal recherché est donc un dépôt d'énergie d'un événement SS avec une énergie centrée sur la Q ββ .

• Bruit de fond externe: radioactivité naturelle des matériaux. Il s'agit de la source principale de bruit de fond pour la recherche de désintégration 0νββ dans

XENONnT. Malgré l'utilisation de matériaux soigneusement choisis en fonction de leur radiopureté, il est impossible de trouver des matériaux complètement exempts de radioactivité. On trouve toujours, même à l'état de trace, des éléments radioactifs à longue durée de vie dans tous les matériaux. Notamment, les longues chaines de désintégration du 238 U, 235 U et 232 Th qui émettent des particules α, β et γ susceptibles de déposer leur énergie (pouvant être proche de Q ββ ) dans le volume sensible du détecteur. Le 60 Co est un autre isotope radioactif présent dans certains matériaux pouvant être une source de bruit de fond pour la désintégration 0νββ . Des mesures de radiopureté des matériaux utilisés pour construire le détecteur ont été effectuées avant sa construction (afin de permettre la sélection des plus radiopurs).

Ces mesures sont aussi nécessaires pour pouvoir exploiter les simulations qui ont été réalisées pour chaque composant du détecteur et chaque isotope radioactif d'intérêt et construire le modèle de ce bruit de fond externe. De plus, ces simulations permettent de définir le volume fiducial optimal pour minimiser la contribution de bruit de fond provenant des matériaux, tout en maximisant l'exposition finale.

• Bruit de fond interne: émission β du 137 Xe. Avec une énergie maximale disponible à 4.17 MeV, bien au-delà de Q ββ , le 137 Xe est une source potentielle de bruit de fond ER pour la recherche de désintégration 0νββ . Il est produit par la capture de neutrons sur le 136 Xe ayant lieu soit à l'intérieur même de la TPC, soit dans les parties non blindées (placées à l'extérieur du réservoir d'eau) où du xénon peut circuler dans différents sous systèmes, tels que les systèmes de purification, sans être protégé du flux de neutrons thermiques ambiants. Il a été déterminé via des simulations MC que les neutrons induits par les réactions de muons dans le LXe sont principalement responsables de la production de 137 Xe dans le TPC. Un modèle analytique a été développé pour décrire la production de 137 Xe dans les systèmes de purification. Ce modèle prend en compte les flux de neutrons thermiques, ainsi que les sections efficaces de capture des neutrons par le 136 Xe, ainsi que les masses de xénon présentes dans chaque systèmes et leurs temps de traversée respectifs.

En effet, ayant une demi-vie courte de 3.8 min, une partie du 137 Xe produit dans les systèmes de purification va se désintégrer avant de pouvoir réintégrer la TPC.

L'estimation de la quantité totale de 137 Xe produit dans les systèmes de purification et la TPC est un élément nécessaire afin de modéliser la contribution précise de ce bruit de fond interne.

• Bruit de fond interne: émission β et γ du 214 Bi. Faisant partie de la chaine de désintégration du Abstract : In the field of particle physics, the search for rare phenomena by means of low background experiments occupies a fundamental place. The nature of dark matter and neutrinos are among the major remaining unknowns in particle physics today. Their understanding is the subject of intense effort by the scientific community and relies on the observation of extremely rare physical processes, such as the direct interaction of dark matter candidates with a detector target and the search for neutrinoless double beta decays. To this end, the XENON collaboration has been developing for several years multiple low background experiments, based on the xenon dualphase time projection chamber technology having as main objective the direct detection of the interaction of weakly interacting massive particle (WIMP) candidate with a xenon target nucleus.

The XENONnT experiment, currently operating in the underground INFN Laboratori Nazionali del Gran Sasso in Italy, is the fourth generation of experiment from the XENON collaboration. Thanks to its unprecedented low level of background and its large target mass of xenon, XENONnT is sensitive to other rare processes, including the search for neutrinoless double beta decay of 136 Xe. In this thesis I will present a first analysis of XENONnT calibration data used to monitor the detector stability during the first scientific run between July and November 2021 and a sensitivity study on the projection for neutrinoless double beta decay search in XENONnT.

  Figure and caption from [2]. . . . . 8 1.4 Solar, atmospheric, and diffuse supernova neutrino fluxes. For the solar fluxes, each individual component is shown. For the atmospheric flux, shown is the sum of all four components (ν e , νe , ν µ , νµ ). For the diffuse supernova neutrino fluxes, shown is the sum of all components (ν e , νe , ν µ , νµ , ν τ , ντ ).

  Figure and caption from [3]. . . . . . . . . . . . . . . . . . 9 1.5 Schematic representation of NR (blue) and ER (red) regions for a bolometer like a germanium detector (left), a liquid xenon TPC (middle) and a liquid argon TPC (right).

19 xi 2 . 2

 1922 Figure and capion from [4] . . . . . . . . . . . . . . . . 12 1.6 Schematic of possible signals that can be measured in direct detection lowbackground experiments depending on the technology in use. Several experiments, mentioned in the coloured boxes and cited in the text, exploit one or two channels using different detector technology. . . . . . . . . . . . 13 1.7 Working principle of common detector types for rare event search with the example of interaction from DM particle (χ) in the case of: (a) scintillating crystal, (b) bolometer (here with additional charge-readout), (c) singlephase and (d) dual-phase liquid noble gas detectors, (e) bubble chamber, and (e) directional detectors. Images adapted from [5]. . . . . . . . . . . . 14 2.1 Repreentation of the Standard Model of particle physics. Particle masses extracted from the Particle Data Group (PDG) [6]. . . . . . . . . . . . . . Feynman diagram of CC leptonic weak interactions, with an exchange of W -(a), W + (b) boson. . . . . . . . . . . . . . . . . . . . . . . . . . . . .

  Figure and caption from [7] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.5 The electron energy spectrum of tritium β decay: (a) complete and (b) narrow region around endpoint E 0 . The β spectrum is shown for neutrino masses of 0 and 1 eV.Figure and caption from [8]. . . . . . . . . . . . . . .

  Figure and caption from [9]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.7 Theoretical spectra of the summed energy of two electrons emitted in 2νββ , 0νββ , and 0νββB modes of the 100 Mo double-β decay. The latter being a particular decay mode,not discussed in this work, involving the emission of a light or massless Goldstone boson, a majoron B. Figure and caption from [9]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.8 Feynman diagrams of 2νββ decay. Figure from [9]. . . . . . . . . . . . . . 2.9 Nuclear-level diagram for the isotope of 100 Mo.

  Figure and caption from [9].

  Figure and caption from [9]. 2.11 Feynman diagrams of 0νββ decay with light Majorana neutrino exchange mechanism. Figure and caption from [9]. . . . . . . . . . . . . . . . . . . . 2.12 Constraints of the parameter space for ⟨m ββ ⟩ in the scenario of three light Majorana neutrinos as function of the lightest neutrino mass m lightest , the sum of neutrino masses m Σ , and the effective neutrino mass m β . Contours follow from a scan of the Majorana phases with the central oscillation parameters from NuFIT 5.1

  Figure and caption adapted from [15]. . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.13 A representative compilation of nuclear matrix element calculations, with an unquenched value of g A = 1.27, for different isotopes. Abbreviations: EDF, energy-density functional; IBM, interacting boson model; QRPA, quasi-particle random-phase approximation; SM, Standard Model. Figure and caption from [16]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

  photographies: XENON Collaboration. . . . . . . . . . . . . . . . . . . . . 3.2 Picture of the XENONnT expriment at hall B of LNGS. The water tank acting as passive shielding and active water Cherenkov muon veto is visible in the background. The detector is safely operating in the center of the water tank as illustrated by the poster covering it. An additional nVeto system is encapsulating the detecor in the water tank, but is not shown in the poster. In the foregroung of the picture we can distinguish the support building containing the various sub-systems of the exeperiments (cryogenic, purification, distilation, recovery, and data acquisition systems). . . . . . . 3.3 After an energy deposition in liquid xenon, different processes lead to ionization, scintillation and heat. The processes indicated by the gray dashed lines are most relevant for recoils resulting in high ionization density. Figure and caption from [24] . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.4 Light and charge yields as a function of drift field for 137 Cs 662 keV γ-rays.

Figure

  Figure and caption from [25] . . . . . . . . . . . . . . . . . . . . . . . . . . 3.5 Schematic view of the time projection chamber working principle. Credit: Lutz Althüser. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.6 Determination of ER (top) and NR (bottom) bands in the (cS1 area, cS2 area) parameter space during XENONnT SR0. The 220 Rn and 241 AmBe calibration data were used to identify the bands, whose median (solid line) and ±2σ percentile are depicted for both ER (blue) and NR (red) type of interaction. The dotted grey lines in the plots show the respective ER and NR energies. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

  Figure and caption from [26]. . . . . . . . . . . . . . . 3.9 Detail view of the anode grid showing the copper pin wire fixtures and the perpendicular wires added to mitigate sagging. Figure and caption from [26] 3.10 A photograph of the neutron veto taken from below the support structure and during its assembly (the bottom octagon was not yet in place). In the center the cryostat covered with ePTFE sheets and the LXe recirculation line are visible. Figure and caption from [26]. . . . . . . . . . . . . . . . . 3.11 Schematic of the XENONnT experiment highlighting the detectors (TPC, Neutron Veto, Muon Veto) as well as the sub-systems for cryogenics and purification. Orange and blue arrows are used to show the path of gaseous and liquid xenon, respectively.Figure and caption from [26]. . . . . . . . . 3.12 Pictures of the electrodes frames (a) and PTFE pillars (b) cleaning in the aboveground cleanroom at LNGS. I am in white suit in the left pictures. .

3. 13

 13 Left: The XENONnT TPC suspended from the top flange of the inner cryostat vessel. It is in a cleanroom inside the XENONnT water tank at the end of the assembly. One panel of the PTFE sheet surrounding the lower part of the TPC was removed to show how the high voltage feedthrough (vertical component made of stainless steel and PTFE) connects to the cathode electrode. Right: PMT arrays during TPC assembly: (top) The top array installed inside the diving bell. (bottom) The cathode electrode is installed above the bottom PMT array. Figure and caption from [26]. . . 3.14 a) Main calibration box, b) Ar branch of the calibration box. Both are connected to the GXe recirculation loop. Credit: XENON collaboration. . 3.15 Illustration of the long-lived radionucleide decay chain of 220 Rn, with decay modes and half-life at each step. This figure is an adaptation of [27], using the updated values from [28]. . . . . . . . . . . . . . . . . . . . . . . . . . 3.16 CAD rendering showing the neutron veto structure and the installed calibration system. In blue the I-belt used to move the Tungsten collimator.

4. 2

 2 Infographic of the signal processing framework used in XENONnT to reconstruct the events with strax(en) in SR0. Details on the plots can be found in the text. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.3 Example waveform from one background event recorded on 20th June 2021. The top row shows the sum waveforms of the main S1 (light blue) and S2 (light green) signals as well as the S1 and S2 hit patterns on the bottom and top PMT arrays, respectively. The bottom panel gives the amplitude of the sum waveform over for the whole event, and indicates the reconstructed times of the S1 and S2 signals with dashed grey lines. . . . . . . . . . . . . 4.4 Decay scheme of 83m Kr.Figure reproduced from

4. 6

 6 Comparison of the S1 b area as a function of the S1 a area parameter space in the range [0, 700] PE for background data (left) and 83m Kr calibration data (right). The different population of 83m Kr events are indicated in black. The primary box selection used to clean-up the 83m Kr data prior to the definition of selection criteria are shown in magenta for the KrDoubleS1 population and in red for the KrSingleS1 population. . . . . . . . . . . . . 4.7 Number of contributing PMTs to S1 a as a function of the S1 a AFT. Selection criteria boundaries are shown in solid black lines, with rejected events under grey bands. The population of gas events is indicated with a red square. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.8 Left: Depth of the interaction as a function of the area seen by the PMT contribtuing the most to the S1 a signal. Selection criteria boundaries are shown in solid black lines, with rejected events under grey bands. Right: Normalized S1 a area distribution for surviving (rejected) events in blue (red). 4.9 Left: Depth of the interaction as a function of the area seen by the PMT contribtuing the most to the S2 a signal. Selection criteria boundaries are shown in solid black lines, with rejected events under grey bands. Right: Normalized S2 a area distribution for surviving (rejected) events in blue (red).

4. 10

 10 Left: S2 b area as a function of the S2 a area parameter space. Three different populations of 83m Kr events can be seen and are identified with colored boxes. Right: Normalized S2 a area distribution for events in each population with matching color. . . . . . . . . . . . . . . . . . . . . . . . . . . .4.11 Reconstructed primary position, on the left column in the (x, y) space and on the right column in the (R 2 , z) space, for 83m Kr events in population 1, 2, and 3 shown in the top, middle, and bottom panel, respectively. . . . . . 4.12 Waveform example of one 83m Kr event from population 1 (top), 2 (middle), and 3 (bottom). For each event, the zoomed waveform for the main S1 and S2, as well as their corresponding PMTs hit pattern are shown on the top part. The waveform of the whole event is shown on the bottom part. S1 peaks are shown in light blue, while S2 peaks are shown in light green. The amplitude of signals are given in PE/ns. . . . . . . . . . . . . . . . . . . . 4.13 Left: S2 a area as a function of the S1 a area parameter space for events surviving the KrSingleS1 selection only. Right: S2 a area as a function of the S1 a area parameter space for events surviving the KrSingleS1 selection and originating from within a FV to remove edge effects. . . . . . . . . . . 4.14 Distribution of the delay time between S1 a and S1 b for events surviving the box selection B shown in figure 4.6. A radioctive decay law function has been fitted to the data between 500 ns and 2000 ns, that resulted in a measurement of the 83m Kr intermediate level half-life of 157.0 ± 0.2 ns. . . 4.15 Top: Distribution scan of the number of contributing PMTs to S1 a (left), S1 b (middle), and number odf distinct PMTs between S1 a and S1 b (right). The distributions structure is divided in three different sub-population highlighted with red, blue and green band. Bottom: Distribution of the delay time between S1 a and S1 b for each sub-population defined in the top row with the corresponding color. . . . . . . . . . . . . . . . . . . . . . . . . . 4.16 Left: S1 a width at 90% of the area as a function of the delay time between S1 a and S1 b . Selection criteria boundaries are shown in solid black lines, with rejected events under grey bands. Right: S1 b width at 90% of the area as a function of the delay time between S1 a and S1 b . Selection criteria boundaries are shown in solid black lines, with rejected events under grey bands. These cuts aim to reject events with merged AP. . . . . . . . . . . 4.17 Left: Distribution of the S1 b rise time after applying all the previous S1 selection criteria. Selection criteria boundaries are shown in solid black lines, with rejected events under grey bands. Right: S1 b width at 90% of the area as a function of the delay time between S1 a and S1 b for events rejected by the cut on S1 b rise time shown in the left panel. Events with AP merged in the S1 b signals are proeprly rejected. . . . . . . . . . . . . . 4.18 S1 b area as a function of S1 a area parameter space for events surviving the KrDoubleS1 selection criteria. . . . . . . . . . . . . . . . . . . . . . . . . . 4.19 Electric field map simulation in SR0 conditions, including the charge of the PTFE reflectors. Figure from [32]. . . . . . . . . . . . . . . . . . . . . . . . 4.20 Spatial distributions of 83m Kr events in the (x, y) space (left), and (R 2 , z) space (right) as reconstructed via the MLP algorithms (top), and after field distortion correction (bottom). The position of the PTFE panels and pillars are depicted in the (x, y) space, while the (R 2 , z) space indicates the cathode position in addition to the PTFE walls as a limitation of the sensitive volume of the TPC. . . . . . . . . . . . . . . . . . . . . . . . . . . 4.21 Relative light yield map across the XENONnT TPC using 83m Kr data. The LCE is averaged out along the azimuthal angle. The top of the TPC is located at z = 0 cm. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.22 Evolution of the median lone-hit area observed in both top and bottom PMTs during SR0. The data points are fitted with a piecewise function made of a constant, linear, and exponential functions applied at different periods of the science run. . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.23 S2(x, y) correction maps for bottom (left) and top (right) PMTs array. Strong variations are observed below the two perpendicular wires where the extraction field distortion affects both SE gain and EE efficiency and near the edge of the TPC where the LCE is worse than in the center. . . . 4.24 Relative SE gain (top) and EE efficiency (bottom) evolutions during XENONnT SR0. The peak structure observed are due anode cycling induce by the appearance of an hot-spot. The colored bands indicates the periods of calibration or non-SR0 operation condition of the detector. . . . 4.25 Electron lifetime measurements using KrSingleS1 events from the 83m Kr calibration of the 6th of September, 2021, with radius smaller than 60.75 cm (to avoid edge effects). The cS2 noEL area corresponds to S2 signals with all correction applied except the electron lifetime one. The distribution of the cS2 noEL area as function of the drift time is divided in 100 µs slice whose cS2 noEL area median is reported as black dot. The median points, within a 200 µs and 2000 µs drift time range (to avoid edge effects), are then fitted with the function from equation 4.5 to measure the corresponding electron lifetime. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.26 Electron lifetime monitoring during XENONnT SR0 with 83m Kr (blue) and 37 Ar (green) calibration data, and intrinsic 222 Rn alpha (red) compared to purity monitor measurements (gray band) from the LXe purification system. The different maintenance operations, inducing a drop in the electron lifetime due to unvolunteer impurity injection, are indicated with dotted lines. The kink in the electron lifetime observed around August is still under investigation but might be related to the start of filter deficiency in the LXe purification system. . . . . . . . . . . . . . . . . . . . . . . . . . . 113 4.27 cS2 area as a function of the cS1 area parameter space for KrSingleS1 events aquired during the 83m Kr calibration of the 6th of September, 2021. The parameter of the 2D gaussian function used to fit the data are illustrated.115 4.28 Measurements of the 32.1 keV (top) and 9.4 keV (middle) LYs with KrDou-bleS1 events acquired during the 83m Kr calibration of the 6th of September, 2021. In both cases, the cS1 distributions are divided into slices as a function of the delay time between the S1 a and S1 b signals. In each slice, the cS1 means is extracted using an iterative fit (bottom). The LYs values are derived from a linear fit of the cS1 means as a function of the delay time between S1s, discussed in detail in the text. . . . . . . . . . . . . . . . . . 118 4.29 Evolution of the cS1 distribution of the 9.4 keV and 32.1 keV (top) signals, and 41.5 keV (bottom) signal from the 83m Kr calibration of the 6th of September, 2021. The median of the distributions is shown as a solid red line, and the 90% (10%) percentile as a dashed (dash-dot) black line. . . . 119 4.30 Top: LYs and CYs monitoring, derived at different energies described in the text, during XENONnT SR0. Bottom: Relative variation of LYs and CYs with respect to the mean value of each mono-energetic line for SR0. The largest variation for both LYs and CYs during the whole science run is given. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122 4.31 Linear fit of the LYs and CYs measured with low-energy mono-energetic

5. 2

 2 Scheme of the electron cloud diffusion and its dependence to depth of the interaction that lead to a z-dependent separation power of the detector from the pile-up of S2s. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.3 Energy spectrum, from MC simulation of 60 Co decay in the SS electrode frames, before (solid blue) and after (solid red) applying the energy resolution function measured in XENON1T. . . . . . . . . . . . . . . . . . . . . 5.4 Energy spectrum of all backgrounds relevant for the 0νββ search in XENONnT. Dominant contributions around Q ββ arise from material backgrounds (solid orange) and, in particular, from 214 Bi in the TPC (solid green), 137 Xe (solid purple) and the LXe shell (dash-dotted green). Backgrounds from 2νββ of 136 Xe (solid blue) and 8 B solar neutrinos (solid pink) are subdominant. The shaded light blue area denotes the 2 σ E ROI. . . . . . . . . . . . . . . . . . 5.5 Summed electrons energy spectra from 0νββ decay MC simulation based on GEANT4 with DECAY0. The spectrum before selections is shown in solid black. The impact of the successive FV and SS selection criteria are shown in dashed blue and dotted red, respectively. . . . . . . . . . . . . . . 5.6 Illustration of the long-lived radionuclides decay chain of 238 U, 232 Th, and 235 U, naturally present in all the materials of the detector, with the decay modes and half-life at each step. This figure is an adaptation of [27], using the updated values from [28]. . . . . . . . . . . . . . . . . . . . . . . . . . 5.7 Rendeing of the XENONnT TPC with identification of the main components of the detector that were studied in the MC study of material backgrounds. The inset elements on the right refers to zoomed parts in the main rendering, without PMTs for clarity. Figure from [38]. . . . . . . . . 5.8 Sensitivity FoM contours in the active volume of the TPC. The (8 × 8) bins segmentation of the (z, R 2 ) parameter space is indiquited with the dashed red lines. The contours used to define the optimal FV are indicated by solid black lines. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.9 Position distribution of simulated material background events in the 2 σ E regions around the Q ββ . The dashed pink line shows the optimized 1088 kg FV. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.10 Energy spectrum of all materials background isotopes. Dominant contributions around Q ββ arise from 226 Ra (solid purple) and 228 Th (solid green), in particular, from 214 Bi high-energy γ at 2447.9 keV. While being close to Q ββ , 60 Co (solid orange) is subdominant. Contribution from 238 U (solid blue), and 232 Th (solid red) are not relevant for the 0νββ decay search. The summed contribution of all isotopes (solid black) correponds to the total materials background model. . . . . . . . . . . . . . . . . . . . . . . . 5.11 Scheme of the 137 Xe decay chain. . . . . . . . . . . . . . . . . . . . . . . . 5.12 Scheme of the XENONnT experiments with the different main systems. The different sources of neutrons that could reach the xenon target are illustrated. The main part of the experiments where 137 Xe could be produced through neutron caputre are indicated with a red square. . . . . . . . . . . 5.13 Toy MC of 137 Xe decay time after its production through the 136 Xe capture of a neutron from a muon crossing the TPC. The time-window necessary to veto 50% (dashed green), 90% (dashed blue), and 99% (dashed red) of those events are shown. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.14 Neutron capture cross-section for 136 Xe (left) and neutron mean free path in natural xenon (right) from [39]. The thermal neutrons (light blue), epithermal neutrons (light orange), and fast neutrons (light red) regimes are overlaid. The peak structures observed are due to nuclear resonances. . . . 5.15 Simplistic illustration of the xenon circulation between the TPC (shielded by the WT) and the three purifiation systems considered in parallel in a non-shielded environment. The production of 137 Xe in the purification systems (green square) is illustrated with red dot. The diminishing number of dots from the purification system up to the TPC (in the orange squares), illustrates the decreasing rate of 137 Xe before reaching the TPC. . . . . . . 5.16 Final 137 Xe energy spectrum with its associated uncertainties. The materials background model is shown for comparison purposes. . . . . . . . . . . 5.17 Energy spectrum induced by 214 Bi decay in the active volume (solid blue) or originating from the LXe shell (solid red) with their associated uncertainties. The summed contribution (solid black) is shown to emphasis the importance of the LXe shell componenet, but will not be used for the background modeling. The two components will be used separately. . . . . . . . 5.18 Normalized energy spectrum for 2νββ decay from MC simulation with DECAY0 (solid blue), Primakoff-Rosen approximation (solid purple), and Kotiala-Iachello theoretical prediction (solid green). The three spectra are in good agreement. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.19 Distribution in energy of the proportion of 2νββ events, from MC simulation with DECAY0, reconstructed as a Single-Site events (black points). A 4PL function was used to fit the data and model the separation power of the detector for 2νββ decay. . . . . . . . . . . . . . . . . . . . . . . . . . . 5.20 Summed electrons energy spectrum from Kotila-Iachello based on the HSD (solid blue) or SSD (solid red) approximations. The relative difference with respect to the HSD model (solid black) is shown in the top panel. . . . . .

  are shown along with the 1σ prediction of the MSW-LMA solution [45] (pink band) accounting for matter effects in the sun. The ν e survival probability without accounting for the matter effect is shown as a grey bands for comparison purposes. . . . . . . . . . . . . . 5.23 Left: Expected rate of 8 B solar neutrino interacting with the xenon target, with its associated uncertainty. Right: Distribution in energy of the proportion of electron recoils, from MC simulation, reconstructed as a Single-Site events (black points). The interpolation of the data (solid red line) used to model the separation power of the detector for neutrino-electron scattering is shown. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.24 Final 8 B solar neutrino-electron scattering energy spectrum with its associated uncertainties. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.25 Sensitivity estimate based on likelihood scan using Asimov dataset with the tested A 0νββ amplitude considering a set experimental livetimes (between 10 days and 1000 days). The log-likelihood ratio reaching the 90 % quantile threshold of a χ 2 distribution denotes the minimal A 0νββ amplitude, and the corresponding half-life, that can be discriminate from the background model with a 90 % C.L. . . . . . . . . . . . . . . . . . . . . . . . . . . . .

  are shown as solid and dashed lines, respectively. . . . . . . . . . . . . . . . . . . . . . . . . . 5.27 Effective Majorana neutrino mass ⟨m ββ ⟩ for XENONnT projection after 1000 days (violet), XENON1T (blue), DARWIN projection after 10 years (dashed blue), and neutrino mass ordering depending on the mass of the lightest neutrino m lightest . The current best experimental limits for different double-β candidate isotopes are shown in the right panel. The values for List of Tables 2.1 Current best results on the 2νββ half-life measurements. Value extracted from [50]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37 2.2 Current best limits on 0νββ search and future perspectives with the next generation of dedicated experiments. . . . . . . . . . . . . . . . . . . . . . 42 3.1 Natural xenon isotopic composition from [51], with indication on the stability of each isotopes. Half-lifes of unstable isotopes are also indicated [52, 53]. 59 3.2 The table summarizes the geometrical properties of five TPC wire electrodes. The vertical positions of the wire planes are given with respect to the gate electrode once the TPC is cooled down to LXe temperature. Table and caption from [26]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66 4.1 List of selection criteria defined to isolate the KrSingleS1 population. The corresponding acceptance of each cut as well as the total acceptance applying them successively is also provided. . . . . . . . . . . . . . . . . . . . . 97 4.2 List of selection criteria defined to isolate the KrDoubleS1 population. The corresponding acceptance of each cut as well as the total acceptance applying them successively is also provided. . . . . . . . . . . . . . . . . . . . . 102 5.1 characteristics of the WIMP and 0νββ decay searches in XENONnT. . . . 127 5.2 Material contamination from screening campaign given in µBq/kg [54]. For the PMTs the contamination level is given in µBq/PMT. The reported contamination for the PMTs is the average contamination of the XENON1T re-used PMTs and the new ones. Upper limits are given if no activity above background was found, in this case, for a conservative approach, these upper limits are considered as a central value with no uncertainty. Components/isotopes whose contamination was not available are excluded from the analysis. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 139 Introduction The Standard Model of particle physics is the modern representation of matter constituents, fundamental building blocks of our Universe, and the physical laws driving their interactions. The predictive power of the Standard Model has been extensively experimentally tested in the past decades, culminating with the discovery of the Higgs boson in 2012. Nevertheless, as often in physics, several unpredicted observations indicate its non-completeness and, thus, the existence of new physics beyond the Standard Model. Aiming to exploit beyond Standard Model physics, this thesis is developed in the frame of rare event physics searches with the XENONnT low background detector. The state of the art of current underground experiments in the context of these searches will be introduced in chapter 1; they include the direct detection of Dark Matter particle interaction, and the observation of neutrinoless double beta decay. Both processes have substantial implications on our comprehension of nature up to the scale of the Universe, as presented in chapter 2, and motivated the tremendous efforts in the scientific community in the last decades to detect them, even though no positive signals have been measured so far. The time projection chambers technology using a xenon target in low-background experiments has shown promising results and played a major role in the field. The XENON collaboration developed a series of experiments based on the xenon dualphase time projection chamber technology, whose main goal is the direct detection of Weakly Interacting Massive Particles -WIMPs (one of the most compelling candidates of dark matter) scattering off a xenon nuclei. XENONnT, the fourth generation of experiments, is currently operating in the underground laboratory of the Instituto Nazionale di Fisica Nucleare (INFN) Laboratori Nazionali del Gran Sasso (LNGS) in Italy. Its design and working principle are presented in chapter 3. The unprecedentedly low background level associated to the ton-scale of xenon target mass achieved in this kind of experiments offers the opportunity to broaden its physics reach, notably towards the search for neutrinoless double beta decay of the 136 Xe isotope naturally present in the xenon target.

Fig. 1 . 1 -

 11 Fig. 1.1 -Illustration of the general principle used to claim the observation of signal events. Data are represented in dotted orange points and compared to the expected energy spectrum from the background only hypothesis (solid blue). The signal expectation is represented by the solid red line, while the signal+background model is indicated by the dashed black line.

Figure 1 . 3 show

 13 the measured muon fluxes in the main DULs hosting low-background experiments as a function of the rock overburden also converted to the equivalent vertical depth of water. The experiment discussed in this work, XENONnT, is hosted by the INFN Laboratori Nazionali del Gran Sasso (LNGS) in Italy, whose underground laboratory is easily accessible by car or truck, implying less constraints in the design/construction of the experiment. Furthermore, muons-veto systems can be used to reduce the muon-induced background further.The second cosmogenic background source of interest for rare event physics searches arises from the astrophysical neutrinos whose most relevant fluxes originate from solar neutrinos, produced through nuclear reaction in the core of the Sun. To second order, neutrinos produced through extensive air shower (named atmospheric neutrinos), or residuals from past supernovae occurring across the universe, so-called diffuse supernova neutrino background (DSNB), could start to be relevant for the next generation of low-background experiments. Neutrinos interact exceptionally weakly with the matter.It is therefore impossible to shield the target from them. Despite the very small crosssection for neutrino interactions, few events are expected to occur due to the very high flux of neutrinos, shown in figure1.4, and must be taken into account. While shielding the target from neutrinos is impossible, experiments that can reconstruct the direction of the incident particle can identify and reject solar neutrino events, exploiting the directionality technique. For experiments unable to use this technique, astrophysical neutrinos ultimately represent an irreducible source of backgrounds.

1 Chapter 1 .

 11 Fig. 1.3 -The measured residual muon fluxes in key underground facilities, which are consistent with predicted values (black line) from [1]. The sizes of the circles correspond to laboratory space by volume; red or blue denotes access by road tunnels or shafts, respectively.Figure and caption from [2].

1 1. 3 .Fig. 1 . 4 -

 1314 Fig. 1.4 -Solar, atmospheric, and diffuse supernova neutrino fluxes. For the solar fluxes, each individual component is shown. For the atmospheric flux, shown is the sum of all four components (ν e , νe , ν µ , νµ ). For the diffuse supernova neutrino fluxes, shown is the sum of all components (ν e , νe , ν µ , νµ , ν τ , ντ ).Figure and caption from [3].

  Fig. 1.4 -Solar, atmospheric, and diffuse supernova neutrino fluxes. For the solar fluxes, each individual component is shown. For the atmospheric flux, shown is the sum of all four components (ν e , νe , ν µ , νµ ). For the diffuse supernova neutrino fluxes, shown is the sum of all components (ν e , νe , ν µ , νµ , ν τ , ντ ).Figure and caption from [3].

1 1. 4 .

 14 Low background experiments

  give rise to three possible signals: heat (phonons), scintillation photons (light) from excited nucleus of the target, or ionisation (charge) of the detection medium atoms, as schematically illustrated in figure 1.6. Detector technologies used in low-background experiments focus either on one or the combination of two of these signals. The leading technologies are also given in figure 1.6, with some examples of experiments using them for DM direct detection (red) or 0νββ decay search (blue).

1 Chapter 1 .

 11 Rare event physics searches

Fig. 1 . 5 -

 15 Fig. 1.5 -Schematic representation of NR (blue) and ER (red) regions for a bolometer like a germanium detector (left), a liquid xenon TPC (middle) and a liquid argon TPC (right).Figure and capion from[START_REF] Marrodán | Dark matter direct-detection experiments[END_REF]

  Fig. 1.5 -Schematic representation of NR (blue) and ER (red) regions for a bolometer like a germanium detector (left), a liquid xenon TPC (middle) and a liquid argon TPC (right).Figure and capion from[START_REF] Marrodán | Dark matter direct-detection experiments[END_REF]

Figure 1 .

 1 Figure 1.5 take the example of physical processes that induces recoils of nucleus or electrons of the target atoms, refered to as nuclear (NR) or electronic (ER) recoils in the following, to illustrates how two different kind of interactions are distributed for some detector technologies and can thus be discriminated.

Fig. 1 . 6 -

 16 Fig. 1.6 -Schematic of possible signals that can be measured in direct detection low-background experiments depending on the technology in use. Several experiments, mentioned in the coloured boxes and cited in the text, exploit one or two channels using different detector technology.

1 Chapter 1 .Fig. 1 . 7 -

 1117 Fig. 1.7 -Working principle of common detector types for rare event search with the example of interaction from DM particle (χ) in the case of: (a) scintillating crystal, (b) bolometer (here with additional chargereadout), (c) single-phase and (d) dual-phase liquid noble gas detectors, (e) bubble chamber, and (e) directional detectors. Images adapted from [5].

1 1. 4 .

 14 Low background experiments decay times induced by different particles.

1 Chapter 1 .

 11 Rare event physics searches

Fig. 2 . 1 -

 21 Fig. 2.1 -Repreentation of the Standard Model of particle physics. Particle masses extracted from the Particle Data Group (PDG) [6].

2 2 Chapter 2 . 2 . 1 . 1 . 2 .

 2222112 Neutrino physics and Dark Matter direct detection Coherent Elastic Neutrino-Nucleus Scattering (CEvNS)

∆m 2 12 > 0 and |∆m 2 23 | ≫ ∆m 2 12 .

 122312 It leads to three possible mass hierarchy scenarios represented in figure 2.4, namely normal ordering (NO): m 1 < m 2 ≪ m 3 and inverted ordering (IO): m 3 ≪ m 1 < m 2 . In the next decade, a new generation of largescale oscillation experiments (DUNE[START_REF] Acciarri | Long-Baseline Neutrino Facility (LBNF) and Deep Underground Neutrino Experiment (DUNE) conceptual design report[END_REF], Hyper-Kamiokande [117], KM3NeT[START_REF] Aiello | Determining the neutrino mass ordering and oscillation parameters with KM3NeT/ORCA[END_REF], and JUNO[START_REF] An | Neutrino physics with JUNO[END_REF]) aims to answer the question of the neutrino mass ordering. Nevertheless, the absolute masses of m 1 , m 2 , and m 3 , are still unknown and cannot be derived from neutrino oscillations experiments. Instead, two different approaches are considered to realize such measurements: direct and inderect measurements.

Fig. 2 . 4 -

 24 Fig.2.4 -The probability that a particular neutrino mass state ν i with mass m i contains a particular charged lepton mass basis state (ν e , ν µ , ν τ ) is represented by colours. The left and right panels of the figure are referred to as normal or inverted mass squared ordering, respectively, referred to as NO or IO. The value of the lightest neutrino mass is presently unknown. Figure and caption from[START_REF] King | Neutrino mass and mixing in the seesaw playground[END_REF]

2 2 2. 1 .Fig. 2 . 5 -

 22125 Fig. 2.5 -The electron energy spectrum of tritium β decay: (a) complete and (b) narrow region around endpoint E 0 . The β spectrum is shown for neutrino masses of 0 and 1 eV. Figure and caption from [8].

29 )

 29 This leads to a light neutrino described by Ψ -whose left-handed component is dominant and a massive neutrino described by Ψ + mostly of right-handed chirality that does not interact (sterile) since m D /m R ≪ 1. Thanks to the see-saw mechanism, we can explain why we observe left-handed neutrino with such a small mass with respect to the other fermions. Nevertheless, it is necessary to have a Majorana neutrino to justify that the see-saw mechanism could explain the neutrino mass's origin and the neutrinos' different properties. Therefore, the identification of the nature of the neutrino, i.e., Majorana or Dirac particle, is of great importance nowadays in neutrino physics. One of the best probe to look for the Majorana nature of the neutrino is the search of violation of the leptonic number, through the detection of the 0νββ decay, introduced in the next section14 .

  [START_REF] Aprile | Energy resolution and linearity of XENON1T in the MeV energy range[END_REF] with ⟨m ββ ⟩ the effective Majorana mass, a linear combination of the neutrino masses m i and the elements of the PMNS mixing matrix given in equation 2.5 for the electronic flavor. It leads to the following decomposition of ⟨m ββ ⟩:

Majorana CP violation phases α 1 , 2

 12 and thus is affected by the uncertainties from oscillation parameters measurements. Nevertheless, it is possible to represents m ββ as function of the lightest neutrino mass (m light )19 for the two mass ordering scenarios. A similar approach can be used to express m ββ as function of the indirect measurements of m Σ from cosmological probe, or as function of the direct measurements of m β from β spectrum experiments, two observables that were introduced in section 2.1.2.2. Figure2.12 shows the three possibles representation of m ββ , with the allowed parameters space from the neutrino mass ordering shown as green (NO) and orange (IO) bands, whose widths come from the uncertainties on the PMNS oscillations parameters in equation 2.38.

2 2 2. 1 .

 221 Introduction to neutrino physics and double weak decay • High detector performance in terms of detection efficiency but also energy resolution in the ROI → enhancing ϵ and decreasing ∆E. Those conditions reflect the requirements satisfied by low-background experiments used in rare-event searches. One particularity of the 0νββ search lies in the definition of ROI near the Q ββ , at the MeV scale. Being this energy higher than the one expected in DM search (order of dozens-hundreds of keV), a low energy threshold is required by experiments designed to look for 0νββ , they instead will favorise detection technologies that allow for optimizing the other factors listed above, i.e., energy resolution, detection efficiency, and exposure.

Fig. 2 .

 2 Fig.2.15 -Temperature power spectrum of the cosmic microwave background (CMB) for a dark matter density contribution ΛCDM varying between 0.11 and and 0.43 (blue lines). All other input parameters of the model are kept constant. The dashed black lines shows the best fit to the Planck data from the 2018 release[START_REF] Aghanim | results[END_REF]. Small (large) multipoles l correspond to lange (small) angular scales: the main acoustic peak at l ∼ 200 is at ∼ 1 • ; l = 1800 corresponds to ∼ 0.1 • . Figure and caption from[START_REF] Schumann | Direct detection of WIMP dark matter: concepts and status[END_REF].

Fig. 2 .

 2 Fig.2.17 -Schematic of the three different approach considered for DM search. The signature of DM production from SM collision at collider, take the form of missing energy. The direct detection looks for signals of relic DM particles scattering off nuclei. The indirect search approach looks for DM annihilation signature from astrophysical objects.

  mate the flux of WIMP crossing the detector. The average local WIMP density ρ 0 = 0.3 GeV/c 2 /cm 3 [172] and the normalised WIMP velocity distribution f (v) are the astrophysical parameters describing the WIMP distribution. The Standard Halo Model used to define the WIMP velocity distribution is based on a Maxwell-Boltzmann velocity distribution. It considers the motion of the Earth around the Sun, the position and motion of the Sun in the galaxy, and the DM gravitational bound. A complete description of this

figure 2 .

 2 figure 2.18, where the expected event rates for WIMPs elastic scattering on various target nuclei are shown. Since the smaller momentum transfer implies smaller recoil energy, the capacity for experiments to lower their energy threshold is a key element to boost their sensitivity to lower WIMPs masses.

Fig. 2 .

 2 Fig.2.18 -Nuclear recoil spectra induced by a m χ = 100 GeV WIMP in various common target materials, assuming a spin-independent WIMP-nucleon cross section σ SI = 1 × 10 -47 cm 2 . The rate for spinindependent interactions increases with A 2 , i.e., prefers heavy target materials. On the other hand, the rate for large nuclei (Xe, I, W) decreases at higher energies due to the form factor suppression. Figure and caption from[START_REF] Schumann | Direct detection of WIMP dark matter: concepts and status[END_REF].

2 2 2. 3 .

 223 Simulatneous search for DM and 0νββ decay in XENONnT the WIMP direct detection search impossible (the notion of neutrino floor used in the past). It is rather a background source whose signature depends on the neutrino source energy and only impacts some specific part of the (σ SI n , m χ ) parameter space, displayed in figure2.19 for xenon target, while the rest remains accessible through larger exposure.

  XENON dark matter program aims at the direct detection of WIMPs employing xenon-based dual-phase Time Projection Chambers (TPC). The XENON experiments have been constructed and were/are operating at the Instituto Nazionale di Fisica Nucleare (INFN) Laboratori Nazionali del Gran Sasso (LNGS) in Italy: an underground laboratory with a 3600 m.w.e depth that reduces the surface muon flux by a factor of 10 6 . At the time of writing this thesis, the XENON collaboration is composed of ∼ 170 scientists from 27 institutions accross 12 countries.

Fig. 3 . 4 -

 34 Fig. 3.4 -Light and charge yields as a function of drift field for 137 Cs 662 keV γ-rays.Figure and caption from[START_REF] Aprile | Liquid xenon detectors for particle physics and astrophysics[END_REF]

. 5 .

 5 A cylindrical TPC is filled with xenon in liquid and gaseous phases. When a particle interacts with the xenon target, light and charge quanta are produced, as mentioned previously. The prompt scintillation light signal (S1) is the first to be detected and determine the starting time of an event. Simultaneously, electrons produced during the interaction will drift towards the GXe phase following a drift electric field, as shown in figure3.5. Slightly below the liquid-gas interface, electrons are accelerated and extracted by a second stronger field (extraction field) in the GXe phase, where they produce an electro-luminescence signal (S2). The great advantage of dual-phase TPCs, compared to single-phase, is this gas amplification step which allows the detection of smaller charge quanta and thus reduces the energy threshold of the detector. The TPC is instrumented with two arrays of photomultipliers (PMTs) at the top and bottom that measure both S1s and S2s signals in photoelectrons (PE). A field cage and series of electrodes are used to apply the drift and extraction fields in the detector as uniformly as possible.Several properties of the interaction can be inferred through the measurements of the S1 and S2 signals. Events position can be reconstructed in three dimensions using the drift time between S1 and S2 to reconstruct the z coordinate and the S2 hit pattern on the top photosensors array for the (x,y) coordinates. Multiplicity of the events can be, to some extent, identified by the number of S2 signals observed. Multiple interactions of the same particle will generate multiple prompt scintillation signals and electron clouds. While only one S1 signal, corresponding to the sum of multiple S1s, can be reconstructed due to the detector dimensions, time resolution, and short photon travel times, multiple S2s can be resolved if they do not overlap. An event with a single S1 and S2 is identified as Single-Site (Single-Scatter, SS) event, while an event with multiple S2s is identified as a Multi-Site (Multiple-Scatter, MS) event. The discrimination between SS and MS events is essential to distinguish between signal and background events 5 .As discussed in section 3.2.1, in XENONnT the discrimination between ER and NR interactions mostly relies on the use of the ratio between light and charge quanta sensors that feature an average quantum efficiency of 34.1% at 178 nm and 20 • C and a collection efficiency of 90%[START_REF] Baudis | Performance of the Hamamatsu R11410 photomultiplier tube in cryogenic xenon environments[END_REF][START_REF] Barrow | Qualification tests of the R11410-21 photomultiplier tubes for the XENON1T detector[END_REF][START_REF] Antochi | Improved quality tests of R11410-21 photomultiplier tubes for the XENONnT experiment[END_REF]. They were developed jointly by Hamamatsu and the XENON collaboration and chosen for their low radioactivity and high quantum efficiency at the xenon scintillation wavelength of 178 nm. The PMTs were distributed in a hexagonal pattern to maximize the number of sensors in the arrays.The drift and extraction fields are applied in the active volume by means of five parallel wire grid electrodes. The cathode (on negative voltage) and gate (around ground potential) electrodes, responsible for the drift field, are placed in the LXe phase at the bottom of the TPC and close to the liquid-gas interface at a distance of 1486 mm. The extraction field is applied between the gate and the anode (on positive voltage) electrodes, the latter being placed in the gaseous phase at a distance of 8 mm from the gate. In addition, two screening electrodes are placed above the anode and below the cathode electrodes and kept at the average bias voltage of all PMTs in the respective array to realize a protective field-free region. The grid electrodes were made of stainless steel parallel wires, whose diameters and pitches (summarized in table

Fig. 3 . 12 -

 312 Fig. 3.12 -Pictures of the electrodes frames (a) and PTFE pillars (b) cleaning in the aboveground cleanroom at LNGS. I am in white suit in the left pictures.

Fig. 3 . 13 -

 313 Fig. 3.13 -Left: The XENONnT TPC suspended from the top flange of the inner cryostat vessel. It is in a cleanroom inside the XENONnT water tank at the end of the assembly. One panel of the PTFE sheet surrounding the lower part of the TPC was removed to show how the high voltage feedthrough (vertical component made of stainless steel and PTFE) connects to the cathode electrode. Right: PMT arrays during TPC assembly: (top) The top array installed inside the diving bell. (bottom) The cathode electrode is installed above the bottom PMT array. Figure and caption from [26].

  As we have seen, different calibration strategies are applied in XENONnT for different purposes: regular bi/tri-monthly calibrations are performed to monitior the detector stability and correct the signals, while before the start or after the end of scientific data taking periods calibrations are performed to characterize ER and NR bands. This leads to strict calibration planning, like the one performed for SR0. While understanding the detector response to the different interactions that can occur is a crucial element, ensuring that the detector behaves stably during the whole science runs is also primordial. Time dependence can easily bias the reconstruction of signals and must be identified and corrected. The monitoring of the S1 and S2 signals reconstruction was also one of the responsibilities carried on during this thesis, and it will be introduced and discussed adequately in section 4.3.

4. 1 .

 1 Signal Reconstruction with the Strax(en) Analysis Frameworks in S1, S2, or unknown signals. These signals are then further splitted by using two algorithms that evaluate the goodness-of-split (GOS) value for each sample of the peaklets: the splitting threshold on the GOS depends on the peak area and signal type. Those classification and splitting procedures are done iteratively until none of the peaklets can be further separated. At this stage, S1 peaklets processing is finalized and S1 peaks are constructed. For S2 peaklets, an additional step is necessary. Indeed, S2 signals have larger widths due to the electron cloud diffusion during their drift. The several iterations of peaklets splitting might cause a break of S2 peaks into small components, especially for events at the bottom of the TPC. Therefore, S2 peaklets are merged back together based on gap time thresholds dependent on the area of the future merged S2 peaklets, whose boundaries were defined using MC simulation. Unknown signals and lone hits falling into the gap time are also merged to the S2 peaklet. This clustering procedure is illustrated in figure 4.2. The results clustered S2 peaklets constitute the final S2 peaks.

  1: S1 classification Peak(let)s with a short rise time, a low AFT, and a tight coincidence of at least two PMTs are classified as S1 signals. The rise time and AFT boundaries are area dependent, as shown in figure 4.2, and were tuned with MC simulation to maximize the S1 reconstruction acceptance.

2 .Fig. 4 . 2 -

 242 Fig. 4.2 -Infographic of the signal processing framework used in XENONnT to reconstruct the events with strax(en) in SR0. Details on the plots can be found in the text.

Fig. 4 . 3 -

 43 Fig. 4.3 -Example waveform from one background event recorded on 20th June 2021. The top row shows the sum waveforms of the main S1 (light blue) and S2 (light green) signals as well as the S1 and S2 hit patterns on the bottom and top PMT arrays, respectively. The bottom panel gives the amplitude of the sum waveform over for the whole event, and indicates the reconstructed times of the S1 and S2 signals with dashed grey lines.

  and S2 signals are referred to as S1 a and S2 a , respectively, while the second largest S1 and S2 signals will be refered to as S1 b and S2 b . The (S1 a , S1 b ) parameter space allows a clear representation of the different population of 83m Kr events according to the number of S1s reconstructed by strax(en).

Figure 4 .

 4 6 shows a comparison of the same parameter space with background data on the left and 83m Kr calibration data on the right. A highlight of the different population of 83m

Fig. 4 . 5 -

 45 Fig. 4.5 -Illustration of differents 83m Kr events topologies reconstructed in XENONnT.

Fig. 4 . 12 -

 412 Fig. 4.12 -Waveform example of one 83m Kr event from population 1 (top), 2 (middle), and 3 (bottom). For each event, the zoomed waveform for the main S1 and S2, as well as their corresponding PMTs hit pattern are shown on the top part. The waveform of the whole event is shown on the bottom part. S1 peaks are shown in light blue, while S2 peaks are shown in light green. The amplitude of signals are given in PE/ns.

  2.1.1, i.e., start to clean up the data sample applying the box cut B, shown in figure 4.6, define cuts on S1 variables, and then focus on S2 variables. Nevertheless, the properties of S2 signals are supposed to be the same in the KrSingleS1 and KrDoubleS1 populations since they correspond in both cases to the pile-up of the electron cloud (from the two subsequent decay) reconstructed4.2.2. Signal correctionAs presented in section 3.2, the detection working principle of a dual-phase TPC such as XENONnT is to measure the light (N γ ) and charge (N e ) quanta produced by an interaction in the sensitive volume of the detector. These quanta are not measured directly but derived from the S1 and S2 signals, detected by the top and bottom PMTs array, that are proportional to the produced light and charge quanta (N γ ∝ S1 and N e ∝ S2). Indeed, several detector effects affect the measurements of the S1 and S2 signals. Their understanding and characterization are required to infer the light and charge quanta produced and extract information regarding the primary interaction. I was not the main responsible for the development of those corrections, but I contributed (through my S1 and S2 stability study discussed in section 4.3) to the identification of time-dependent behavior of the signal reconstruction, that motivated the development of new correction at the function of time. Among the various detector effects impacting the S1 and S2 signals measurements that will be introduced in section 4.2.2.2 and section 4.2.2.3 respectively, some of them are by nature dependent on the position of the signal generation vertices. However, the reconstruction of the position relies on the measurements of the S1 and S2 signals, as presented in section 4.1, and thus can also be affected by detector effects. Therefore, a dedicated correction of the observed reconstructed position is required before correctiong the signals for others effects.

Fig. 4 . 19 -

 419 Fig. 4.19 -Electric field map simulation in SR0 conditions, including the charge of the PTFE reflectors. Figure from [32].

2 . 2 . 1 ,

 221 figure 4.21. This map includes all the detector effects mentioned above, not only the S1 LCE, in order to correct the S1 signal and build the cS1 variable that can be expressed from equation 4.1 as:

2 )

 2 Light yield time dependence: The relative light yield map allows for correcting only the spatial dependence of the S1 signals. Nevertheless, a variation of the measured signal subject to local distortion, leading to a spatial dependence of the electron extraction (EE) efficiency, noted ϵ ext .

1 .

 1 As it was already introduced in section 3.4, single electron bursts (also called hotspots) have appeared close to the anode during SR0. Their presence motivated the need to switch off and on again the anode, causing a disequilibrium in the extraction field that took time to return to stable conditions. The induced warping in electrodes, impacted the EE efficiency and SE gain after each anode cycle, during the whole SR0 period. Their evolution is shown in figure4.26 where a consistent result among the three internal sources and the purity monitor can be observed. The EL trends during SR0 exhibit several sharp decreases that coincide with releases of impurities due to operations on the xenon cryogenics and purifications systems18 . Furthermore, constant outgassing of the materials and limited xenon circulation flow in the purification systems induced a leveling off of the EL after some time. The EL measurements from 83m Kr and 222 Rn data were used together to model the observed trends, as represented with a magenta dashed line in figure4.26.

4 .

 4 In the context of this thesis, I was in charge of their monitoring during SR0, with multiple internal calibration sources. This work has been performed within an analysis group where I was responsible for the coordination. Therefore, part of this work has been performed in collaboration with J. Loizeau (PhD at SUBATECH), Y. Ma (PhD at UCSD), Y. Xing (Postdoc at SUB-ATECH), M. Bazyk (PhD at SUBATECH), D. Cichon (Postdoc at MPIK of Heidelberg), and K. Bui (Postdoc at University of Tokyo). My personal contributions to this task are the following:

4. 3 . 2 . 2 . 3 .

 3223 figure 4.28.

figure 4 . 28 .•

 428 figure 4.28. They are due to possible reconstruction bias from the presence of AP, issue in splitting the tail of the S1 a peak due to the presence of the S1 b peak, and fewer statistics. The delay time range for the linear fit is thus constrained to 1000 ns. The cS1 a delay time range for the fit is [450, 1000] ns. • The cS1 b (9.4 keV) peak is more subject to AP contamination as discussed in section 4.2.1.2. This leads to upper fluctuations of cS1 b with a delay time between S1s close to 500 ns (from He AP contamination) as it can be observed in the middle panel of figure 4.28. In order to exclude this fluctuations, the

  Co at 1173 keV and 1332 keV, 40 K at 1764 keV, and 214 Bi at 2225 keV. The result of the LY and CY time stability study for all those calibration sources is summarized in figure 4.30, where the top panel shows the evolution of the LY and CY absolute values during SR0, while the bottom panel shows the relative variation for the mean value for each mono-energetic line and KrDoubleS1 S1 signals. Both LY and CY were steadily stable during the whole science run, within 1% for the LY and 3% for the CY, especially during the blinded data-taking period (post-July) where the CY variation droped below 2%. A strong fluctuation can be seen during the 4.4. Energy reconstruction

Chapter 5 136

 5 5 keV thats corresponds to the binding energy of deuterium during the AmBe calibration, can bias the corresponding LY and CY measurements. The validation and improvements of the signal reconstruction towards higher energy analyses including the 0νββ decay search with XENONnT data, is one of the next analysis goals post-SR0. The work presented in the next chapter is preparatory for this search in XENONnT. Xe 0νββ sensitivity projection study in XENONnT Experiments developed by the XENON collaboration are designed to search for WIMP DM candidates and optimized to work in the few keV electron recoil energy range. To allow the XENON experiments to search for DM and 0νββ decay of 136 Xe simultaneously, several improvements must be made in the MeV region, especially concerning the reconstruction and correction of high energy signals.

  PhD students and postdocs belonging to different institutions of the XENON Collaboration, namely C. Capelli (PhD at the University of Zurich), A. Rocchetti (PhD at the University of Freiburg), E. Masson (Postdoc at LPNHE), C. Wittweg (PhD at the University of Münster), and T. Wolf (Postdoc at the MPIK of Heidelberg). My main task consisted in studying the internal backgrounds to evaluate their specific impact on the search of 0νββ events and in the modelization of the expected signal. The final version of the analysis has been published as part of a XENON collaboration paper dedicated to the search for Double-Weak Decays of 124 Xe and 136 Xe in the XENON1T and XENONnT

5. 1 .ΔZFig. 5 . 2 -

 152 Fig.5.2 -Scheme of the electron cloud diffusion and its dependence to depth of the interaction that lead to a z-dependent separation power of the detector from the pile-up of S2s.

5. 1 .

 1 Context of the 0νββ decay projection study for XENONnT

Fig. 5 . 7 -

 57 Fig. 5.7 -Rendeing of the XENONnT TPC with identification of the main components of the detector that were studied in the MC study of material backgrounds. The inset elements on the right refers to zoomed parts in the main rendering, without PMTs for clarity. Figure from [38].

  25 yr at 90 % CL for a livetime of 1000 days. While not being competitive with current best limits from experiments dedicated to 0νββ decay search, such result demonstrates the feasability to search for this rare process at the MeV energy scale with an experiment primarly designed for Dark Matter search at lower energies (O(50) µkeV). This motivates the broadening of physics goals reachables by the next generation of experiments, like DARWIN, foreseeing a larger xenon target of the order of 50 tonnes.The study presented in this thesis allowed to identify the different limiting factors in terms of background impacting the sensitivity of XENONnT on the neutrinoless double beta decay process that must be taken into account for the next generation of experiments using the same technology, in order to reach competitive. Notably, the choice of radiopure materials for the cryostats with a precise estimation of their contamination level and the shielding of sub-systems with a large amount of xenon outside of the water tank may allow to further suppress neutron activation products such as the137 Xe isotope which represents one of the main source of intrinsic background in the region of interest. The impact of this source of background has been studied for the first time in the context of a XENON experiment. Another important part of the work presented in this manuscript consists in the monitoring of the detector stability during data taking and in the implementation of signals corrections. This is of fundamental importance to ensure the good quality of data that are used for the different searches performed by the XENON collaboration. The 83m Kr calibration data, acquired during the first science run (SR0) of XENONnT, has been used, thanks to the selection criteria defined in this work, to build signal corrections necessary to account for detector effects impacting their measurements. The stability of the light (LY) and charge (CY) yields of XENONnT during SR0 has been studied with different mono-energetic calibration sources at different energies. This study concluded a stable condition during the blinding data acquisition over a duration of 7 months, with varia-A.1. Contexte et motivations secondaires produites sont atténuées après quelques mètres de profondeur. Cependant certaines particules très pénétrantes, telles que les muons, nécessitent plusieurs centaines de mètres de roches afin de réduire leur flux de manière significative, et l'utilisation de systèmes de veto peut rester nécessaire. Un second type de bruit de fond cosmogénique, celui-ci étant irréductible, existe. Il s'agit des neutrinos d'origine astrophysique, provenant principalement du soleil, qui interagissent très faiblement avec la matière mais dont le flux très important peut engendrer des interactions dans l'expérience.

  de réconcilier les prédictions théoriques et les observations, il est nécessaire d'introduire une nouvelle forme de matière, la Matière Noire, qui ne serait pas directement visible mais qui interagirait gravitationnellement avec la matière baryonique. La MN représenterait 85% de la densité de masse totale présente dans notre Univers. Grâce à ces observations, on peut en déduire les différentes propriétés que doit satisfaire la MN. Elle doit être une matière non lumineuse (pas d'interaction électromagnétique), massive (pour expliquer son impact gravitationnel), non relativiste (afin d'expliquer la structure de l'Univers visible actuel), stable ou avec une demi-vie extrêmement longue (car elle est toujours visible dans notre Univers actuel), et elle doit interagir très faiblement avec la matière baryonique et elle-même. Une pléthore de particules candidates à la MN, satisfaisant ces propriétés, ont été théorisées au cours des dernières décennies. L'une des familles de particules les plus étudiées est celle des WIMPs (Weakly Interacting Massive Particles -Particules Massives Interagissant Faiblement), qui inclut des particules prédites par des théories au-delà du Modèle Standard, telles que la supersymétrie. L'intérêt pour les WIMPs réside dans leur capacité à expliquer naturellement l'abondance de matière noire observée dans notre Univers, si leur section efficace d'annihilation est de l'ordre de grandeur de l'interaction faible (phénomène appelé le "miracle des WIMPs"). La gamme de masse prédite pour les WIMPs se situe entre le GeV et le TeV. D'autres familles théoriques de candidats pour la Matière Noire existent, mais dans le contexte de cette thèse, nous nous concentrerons sur le cas des WIMPs et des approches expérimentales développées pour les détecter. Trois approches principales sont utilisées pour observer les WIMPs autrement que par leur impact gravitationnel : leur production lors de collisions de particules du MS dans des accélérateurs, la détection indirecte de la signature d'annihilation ou désintégration de WIMPs à partir d'objets astrophysiques, et la détection directe de WIMPs diffusant élastiquement avec des particules du MS dans des expériences terrestres. La dernière méthode est celle sur laquelle se basent les expériences à faible bruit de fond, telles que XENONnT. Elle repose sur l'idée que la Terre se déplace constamment dans un halo de MN entourant notre galaxie. Ainsi, dans le référentiel terrestre, un vent de particules de MN traverse notre planète 5 . L'interaction attendue dans notre détecteur est une diffusion élastique d'un WIMP avec un noyau cible. L'énergie de recul nucléaire dépend de la masse du WIMP, du noyau cible et de la vitesse du WIMP. La plage d'énergie attendue est située à faible énergie, entre 1 et 100 keV. Une description plus détaillée des mécanismes d'interaction est proposée dans le corps du manuscrit. Toutefois, il est important de souligner que le choix du noyau cible influence directement le taux d'événements attendus. Le xénon offre un excellent équilibre entre le taux d'événements prévus et la capacité de détection (seuil en énergie bas) dans cette gamme d'énergie. La technologie des chambres à projection temporelle bi-phasée au xénon, telle que celle employée dans l'expérience XENONnT, a démontré son rôle majeur dans la recherche de détection directe des WIMPs en imposant les meilleures limites sur la section efficace d'interaction WIMP-nucléon dans une gamme de masse comprise surpasser les limites établies par les générations précédentes. Il est important de souligner que l'une des grandes réussites du programme XENON a été la démonstration de la scalabilité de la masse cible avec les TPC à double phase au xénon et la suppression significative du taux de bruit de fond observé dans le détecteur. Cela permet une amélioration de la sensibilité d'au moins un ordre de grandeur d'une génération de détecteur à la suivante.Le xénon présente de nombreux avantages pour les expériences de recherches d'événements rares, grâce à ses propriétés physiques qui permettent son utilisation comme cible et milieu de détection.

A. 4 .••••

 4 AmBe ayant pour objectif de caractériser la réponse du détecteur pour des NR. L'utilisation du veto à neutron pour identifier une coïncidence avec l'émission d'un γ de 4.4 MeV par la source, permet une sélection propre des neutrons interagissant dans la TPC. L'utilisation de ces sources d'étalonnage, notamment celle de 83m Kr, est une composante importante des travaux effectués dans le contexte de cette thèse qui fait l'objet de la prochaine section. Reconstruction et suivi des signaux lors du Science Run 0 de XENONnT L'étalonnage du détecteur est un élément crucial afin de pouvoir exploiter les mesures effectuées et rendre possible la recherche d'événements rares tels que la MN ou la désintégration 0νββ . Une partie des travaux entrepris durant cette thèse a été de participer à la mise en place de la stratégie d'étalonnage du détecteur en développant des outils d'analyse afin d'exploiter les données des périodes de calibration au 83m Kr. Ces données sont la clé de voûte permettant de caractériser et corriger les effets du détecteur impactant la mesure des signaux S1 et S2. Ces travaux ont été effectués dans le cadre du SR0 de XENONnT et sont résumés sommairement en trois axes principaux ci-après. Pour une description plus détaillée de ces travaux, le lecteur peut se référer au chapitre 4 de ce manuscrit. Il y trouvera notamment une description de la logique de l'algorithme de traitement des données straxe(en), développé par la collaboration XENON. Cette étape de traitement des données est primordiale afin de pouvoir fabriquer, à partir des signaux individuels mesurés par les PMTs, les différentes structures de plus haut niveau (peaklets, peaks) nécessaires à la reconstruction des événements (paires de signaux S1 et S2) induits par une interaction physique dans la TPC. La sélection des événements 83m Kr : Cette source de calibration interne, comme décrit précédemment, est caractérisée par deux transitions successives à 32.1 keV et 9.4 keV, principalement par conversion interne (CI). La demi-vie de 156.8 ns du niveau intermédiaire induit une signature particulière de la source d'étalonnage de 83m Kr. En comparaison avec la largeur temporelle typique des signaux S1 et S2, d'environ O(100) ns et O(1) µs respectivement, la demi-vie intermédiaire est telle que la discrimination du signal entre les deux étapes de désintégration par strax(en) n'est pas toujours possible pour les S1s et extrêmement difficile pour les S2s. Cette caractéristique de la source de 83m Kr implique l'existence de trois topologies d'événements différents. Les événements avec deux S1 et deux S2 distinguables (9.4 keV et 32.1 keV), appelés KrDoubleS1S2, extrêmement rares de par la difficulté à distinguer les deux signaux S2 en raison de l'ordre de grandeur de leur largeur temporelle mentionnée précédemment. Les événements avec deux S1 séparés (9.4 keV et 32.1 keV) et un seul S2 correspondant à l'empilement des deux signaux d'ionisation (41.5 keV), appelés KrSingleS1S2, et enfin les événements avec un seul S1 et S2 correspondant à l'empilement des signaux d'ionisation et de scintillation des deux CI successives (41.5 keV), appelés KrDoubleS1SingleS2. L'objectif principal du travail effectué pour cette tâche a été de mettre en place une procédure de sélection des différentes topologies d'événements 83m Kr permettant de maximiser l'acceptance d'événements ne montrant pas de biais de reconstruction évident. Pour ce faire, différentes propriétés des signaux S1 et S2, telles que leurs amplitudes (area), temps de montée (rise time), proportion de lumière vue par le réseau de PMTs du haut (area fraction top) et autres, ont été étudiées afin de définir une série de critères de sélection optimale. Cette étude a permis la mise en place de critères de sélection pour les populations de KrSingleS1S2 et KrDoubleS1SingleS2 avec une acceptance finale de 51.6% et 8.34% respectivement. Ces critères de sélection sont largement utilisés au sein de la collaboration afin d'étudier et corriger les différents effets de détecteurs affectant la mesure des signaux S1 et S2. Correction des signaux S1 et S2 : Comme introduit dans la section A.3, le principe de fonctionnement de détection d'une TPC telle que XENONnT consiste à mesurer les quanta de lumière (N γ ) et de charge (N e ) produits par une interaction dans le volume sensible du détecteur. Ces quanta ne sont pas mesurés directement mais dérivés des signaux S1 et S2, enregistrés par les réseaux de PMTs, qui sont proportionnels aux quanta de lumière et de charge produits (N γ ∝ S1 et N e ∝ S2). En effet, plusieurs effets du détecteur, énumérés ci-dessous, affectent les mesures des signaux S1 et S2. Leur compréhension et leur caractérisation sont nécessaires pour déduire les quanta de lumière et de charge produits et extraire des informations concernant l'interaction primaire. Je n'étais pas le principal responsable du développement de ces corrections, mais j'ai contribué (grâce à mon étude de stabilité des signaux S1 et S2 discutée par la suite) à l'identification de variations temporelles de la reconstruction du signal, ce qui a motivé le développement de nouvelles corrections dépendantes du temps. • Correction de la position observée : Parmi les différents effets du détecteur impactant les mesures des signaux S1 et S2 qui seront présentés par la suite, certains dépendent de la position de l'intéraction primaire. Cependant, la reconstruction de la position repose sur les mesures des signaux S1 et S2 et peut donc également être affectée par les effets du détecteur. Par conséquent, une correction dédiée de la position observée est nécessaire avant de pouvoir corriger les signaux pour d'autres effets qui dépendraient de la position. Malgré les efforts déployés pour obtenir un champ de dérive le plus uniforme possible, des distorsions des lignes de champ peuvent exister, induisant un transfert de la position primaire vers une position observée différente (position de l'extraction du nuage d'électrons dans la phase gazeuse). En supposant une uniformité spatiale des évènements de 83m Kr (ce qui est attendu pour une source d'étalonnage interne), une carte de correction (3D) de la position a été construite pour corriger les effets de la non-uniformité du champ de dérive. Carte d'efficacité de la collection de lumière des signaux S1 : Lorsqu'une interaction se produit dans la cible de LXe, l'intégralité des photons produits lors du signal de scintillation rapide ne sont pas détectés par les PMTs. En effet, une partie de ces photons peut être absorbée par des impuretés présentes dans le xénon ou les matériaux de la TPC (parois en PTFE, électrodes en acier). De plus, même si les photons atteignent un PMT, il est nécessaire de prendre en compte l'efficacité de détection de ce PMT. Tous ces effets pouvant atténuer la mesure du nombre de photons émis au point d'intéraction dépendent fortement de la position de l'évènement primaire. Pour corriger cet effet, une carte de correction (3D) de l'efficacité de la collection de lumière des signaux S1 a été construite en utilisant la population KrS-ingleS1S2 qui, en moyenne, est censée produire le même nombre de photons (en tenant compte des fluctuations du phénomène de recombinaison) dans un détecteur parfait. Dépendance temporelle des signaux S1 : Il s'avère qu'en plus de la dépendance spatiale mentionnée précédemment, une évolution de l'amplitude moyenne mesurée par les PMTs a été observée lors du SR0 de XENONnT. Cette dépendance temporelle est liée à une instabilité du détecteur ayant plusieurs origines. Premièrement, une évolution de la pression et de la température au sein de la TPC a été observée lors de la période de calibration qui a eu lieu avant la prise de données scientifiques. De plus, il était nécessaire d'éteindre les PMTs lors de certaines opérations sur le détecteur, et lors de leur remise en route, un certain temps était nécessaire pour revenir à des conditions de fonctionnement stables. Une correction dédiée a été mise en place pour corriger ces effets. Dépendance spatiale de la mesure de charge : Les charges extraites lors d'une interaction sont sujettes à des effets différents de la lumière de scintillation prompte.Ces effets comprennent l'attachement des électrons aux impuretés électro-négatives présentes dans le xénon liquide, ce qui atténue le signal S2 en fonction du temps de dérive. De plus, une partie des électrons reste piégée au niveau de l'interface liquide-gaz, réduisant davantage les signaux S2. Cette efficacité d'extraction des électrons dépend également des distorsions locales du champ d'extraction, entraînant une dépendance spatiale. Une fois extraits dans la phase GXe, les électrons génèrent des photons par le processus d'électroluminescence, dont le nombre moyen produit par électron extrait correspond au gain de scintillation secondaire (SE gain), qui dépend du champ d'extraction et de l'épaisseur de gaz entre l'interface liquide-gaz et l'anode. Ce processus crée également une dépendance spatiale. De manière similaire au signal S1, la fraction de photons, générés dans le processus d'électroluminescence, atteignant la photocathode du PMT est également affectée par les effets de propagation de la lumière. Enfin, les photons atteignant la photocathode des PMTs sont soumis à la même variation de réponse des PMTs, induite par l'efficacité de collection et de quantification des photons. Il est possible de séparer ces effets en deux composantes avec des dépendances spatiales indépendantes : une première dépendant uniquement de la profondeur de l'interaction (liée aux impuretés présentes dans le LXe), et une autre liée au plan (x, y) de la phase gazeuse où les signaux S2 sont produits. Pour la dépendance spatiale liée à la profondeur de l'interaction, celle-ci est corrigée via la mesure de la durée de survie des électrons lors de leur dérive dans le LXe, à l'aide des évènements 83m Kr. Pour ce qui est de la dépendance spatiale liée à l'extraction des électrons dans la phase gazeuse et à la production/mesure du signal S2, une approche similaire à celle utilisée pour la dépendance spatiale des signaux S1 a été utilisée. Dépendance temporelle de la mesure de charge : La mesure des signaux S2 souffre également d'une dépendance temporelle, que ce soit lié à l'évolution du niveau de pureté dans le LXe ou induit par les changements de conditions dans la phase gazeuse impactant l'efficacité d'extraction des électrons et le gain de scintillation secondaire. Ces différents paramètres pouvant être mesurés et suivis durant la période de prise de données, des corrections ont pu être développées de manière appropriée.

L

  'outil de simulation de la collaboration XENON, permet de simuler le signal étudié et les différentes sources de bruit de fond d'intérêt qui y sont associées. Pour chaque événement simulé, les dépôts d'énergie dans le volume sensible du détecteur (et d'autres propriétés) sont enregistrés. Dans un second temps, un traitement de ces données MC est effectué afin d'inclure les effets des détecteurs principaux, tel que la résolution en énergie et le pouvoir de séparation de ce dernier. La dernière étape consiste à calculer le temps de vie effectif correspondant à chaque série de simulation effectuée. Cette observable permet de déterminer l'équivalent en temps d'exposition de l'expérience pour obtenir une statistique équivalente à ce qui a été simulé. Cela est nécessaire afin de pouvoir exploiter ces simulations pour construire les spectres en énergie avec le taux d'événements attendus pour chaque source de bruit de fond.

8 B.

 8 Pour ce faire, le phénomène d'oscillation des saveurs des neutrinos (incluant les effets de matière dans le soleil) doit être pris en compte afin de déterminer le flux de neutrinos électroniques atteignant le détecteur. Le flux total de neutrinos mesuré par l'expérience SNO a été utilisé dans cette étude. La forme du spectre en énergie induite par diffusion élastique neutrino-électron a été calculée de manière analytique, en incluant les effets de détecteur via simulation MC. Grâce aux études des différents bruits de fond effectuées dans cette thèse, il a été possible de déterminer pour chaque source le taux d'événements attendus dans la région d'intérêt de la 0νββ . Ces modèles de bruit de fond ont été utilisés pour estimer la sensibilité de XENONnT pour la recherche de désintégration 0νββ . De plus, ces études ont permis de déterminer les bruits de fond dominants pour cette recherche dans XENONnT (provenant des matériaux), qu'il sera nécessaire d'atténuer pour les futures générations d'expériences afin d'améliorer leur sensibilité pour ce canal de recherche. J'ai aussi pu identifier une source potentielle de bruit de fond qu'il sera nécessaire de prendre en compte dans la conception des futures expériences si elle devient dominante, à savoir la production de 2νββ du 137 Xe dans les systèmes de purification du xénon. La sensibilité de XENONnT pour la recherche de désintégration 0νββ du 136 Xe, pour une durée d'acquisition de 1000 jours, a été estimer a: Titre : Recherche de désintégration double beta sans émission de neutrinos avec XENONnT. Mots clés : décroissance double beta sans émission de neutrinos, matière noire, xénon, XENONnT Résumé : Dans le domaine de la physique des particules, la recherche de phénomènes rares par des expériences à bas bruit de fond occupe une place fondamentale. La nature de la Matière Noire et des neutrinos figurent parmi les principales inconnues subsistantes en physique des particules de nos jours. Leurs compréhensions sont l'objet d'efforts intenses de la part de la communauté scientifique et repose sur l'observation de processus physiques extrêmement rares, tel que l'interaction directe de particules candidates au rôle de Matière Noire avec la cible d'un détecteur et la recherche de désintégration double beta sans émissions de neutrinos. Dans cette optique la collaboration XENON développe depuis plusieurs années de multiples expériences à bas bruit de fond, basées sur la technologie de détection de chambre a projection temporelle double phase au xénon et ayant pour objectif principal la détection directe de l'interaction d'une particule massive interagissant faiblement (WIMP) avec un noyau cible de xénon. L'expérience XENONnT, actuellement en activité au sein du laboratoire souterrain de l'INFN Laboratori Nazionali del Gran Sasso en Italie, est la quatrième génération d'expérience de la collaboration XENON. Grâce à son environnement de bas bruit de fond sans précédent et à sa grande masse cible de xénon, XENONnT est sensible à d'autres processus rares, dont la recherche de désintégration double beta sans émissions de neutrinos du 136 Xe. Dans cette thèse, je présenterai une première analyse des données de calibration de XENONnT utilisées pour surveiller la stabilité du détecteur lors de la première période d'acquisition de données scientifiques entre juillet et novembre 2021 et une étude de la sensibilité pour la recherche de désintégration double beta sans neutrinos attendues dans XENONnT. Title : Neutrinoless double beta decay search with XENONnT. Keywords : neutrinoless double beta decay, Dark Matter, xenon, XENONnT

1

  1.3. Backgrounds sources and mitigation strategies over more than 10 orders of magnitude in energy, from 10 9 to 10 21 eV, and 30 in flux, which quickly decreases as a function of the energy from 1 particle/m 2 /s at 10 11 eV to less than 1 particle/km 2 /century at 10 20 eV[START_REF] Beatty | The highest-energy cosmic rays[END_REF]. When a cosmic ray reaches the atmosphere, it interacts with nuclei in the air producing a cascade of secondary particles through subsequential interactions, as illustrated in figure1.2. This phenomenon, called an extensive air shower, can produce at sea level large numbers of particles, mostly gammas, e ± , and muons.

Low-background experiments are located in deep underground laboratories (DUL)

  Among the most studied isotopes, the136 Xe is of particular interest in the context of this thesis. Currently holding the most stringent limit on the effective Majorana mass, thanks to KamLAND-Zen measurements, this isotope offers the possibility to scale the target mass effectively and motivates the development of future experiments based on the xenon TPC detection technology, such as nEXO or NEXT-HD. Interestingly, xenon-based

The current best limit on 0νββ decay half-life and effective Majorana mass from dedicated experiments studying those isotopes are summarized in table 2.2. The detection technology used is also reported (for the overview on low background experiments technologies, see section 1.4). As shown in figure 2.12, the current constraints on the effective Majorana mass are only at the onset of the neutrino mass IO. The aim of the next generation of 0νββ decay experiments also reported in table 2.2 and currently under development, is to probe and completely cover the neutrino mass IO.

Table 2 .

 2 2: Current best limits on 0νββ search and future perspectives with the next generation of dedicated experiments. 0ν 10 25 yr ⟨m ββ ⟩ [meV] Ref.

	Isotope S Current best results Experiment Technology
	76 Ge	GERDA	Ge diodes	18	79 -180	[47]
		MAJORANA	Ge diodes	8.3	113 -269	[147]
	82 Se 100 Mo 130 Te	CUPID-O CUPID-Mo CUORE	Scint. bolometers Scint. bolometers Cryo. bolometers	4.6 × 10 -1 1.5 × 10 -1 2.2	263 -545 310 -540 90 -305	[148] [49] [48]
	136 Xe	KamLAND-Zen Liq. Scintillator	23	36 -156	[12]
		EXO-200	LXe TPC	3.5	78 -239	[35]
	Future experiments
	76 Ge 100 Mo 136 Xe	LEGEND-1000 CUPID nEXO NEXT-HD	Ge diodes Cryo. bolometers LXe TPC GXe TPC	1.2 × 10 3 1.1 × 10 2 1.35 × 10 3 1.7 × 10 2	10 -20 12 -20 4.7 -20.3 13 -57	[149] [?] [150] [149]

Table 3 .

 3 1: Natural xenon isotopic composition from [51], with indication on the stability of each isotopes.Half-lifes of unstable isotopes are also indicated[START_REF] Aprile | Double-weak decays of 124 Xe and 136 Xe in the XENON1T and XENONnT experiments[END_REF][START_REF] Albert | Improved measurement of the 2νββ half-life of 136 xe with the EXO-200 detector[END_REF].

	Isotope Abundance [%] Decay mode	Half-life [years]
	124 Xe 126 Xe	0.09 0.09	2νECEC stable	(1.1 ± 0.2 stat ± 0.1 sys ) × 10 22 -
	128 Xe	1.92	stable	-
	129 Xe	26.4	stable	-
	130 Xe	4.08	stable	-
	131 Xe	21.2	stable	-
	132 Xe	26.9	stable	-
	134 Xe	10.4	stable	-
	136 Xe	8.87	2νββ	(2.165 ± 0.016

stat ± 0.059 sys ) × 10

21

The scintillation and ionization properties of LXe also allow using it as an efficient detection medium. A rare event inducing an energy deposition in gas or liquid xenon can occur through two types of interaction: it can either scatter off xenon nuclei (in the case of WIMPs, neutrons, or neutrinos) or atomic electrons (γ rays, charged particles, and neutrinos), generating Nuclear (NR) or Electronic Recoils (ER), respectively.

The transferred energy from the recoil will produce heat, excitation (Xe * , also called excitons), and ionization (Xe + ), as depicted in figure

3

.3. Only the latter two yield detectable signals in dual-phase TPCs. Through collisions with other xenon atoms, Xe * form excited molecular states, called dimers (Xe * 2

Table 3 .

 3 2:The table summarizes the geometrical properties of five TPC wire electrodes. The vertical positions of the wire planes are given with respect to the gate electrode once the TPC is cooled down to LXe temperature. Table and caption from[START_REF] Aprile | The XENONnT dark matter experiment[END_REF].

	TPC Electrode	Wire Diameter Wire Pitch Optical Transparency Vertical Position
	Top screening	216 µm	5 mm	95.7 %	+36 mm
	Anode	216 µm	5 mm	95.7 %	+8 mm
	Gate	216 µm	5 mm	95.7 %	0 mm
	Cathode Bottom screening 216 µm 304 µm	7.5 mm 7.5 mm	96.0 % 97.0 %	-1486 mm -1541 mm

Xenon recovery and storage systems

  and reused in XENONnT to reach concentrations as low as nat Kr/Xe ∼ 50 ppq (mol/mol). For XENONnT a new radon distillation was developed and succeeded in reaching a222 Rn activity < 1µBq/kg[START_REF] Aprile | XENONnT: Radon removal paper[END_REF].The storage, filling, and recuperation of the xenon inventory is handled by two dedicated xenon-storage systems called ReStoX (Recovery and Storage of Xenon). The first unit, ReStoX1, was designed and constructed for XENON1T[START_REF] Aprile | The XENON1T dark matter experiment[END_REF]. It consists of a vacuuminsulated stainless-steel sphere conceived to store up to 7.6 tonnes of xenon either in liquid or gas phase, to fill the xenon into the detector vessel in ultra high purity conditions, and to ensure fast recovery of xenon. Its capacity is insufficient for the larger xenon inventory of XENONnT (8.3 t), a second unit, i.e. ReStoX2, has been designed to operate alongside the first unit[START_REF] Aprile | The XENONnT dark matter experiment[END_REF]. ReStoX2 can store 10 tonnes of xenon at room temperature and can achieve fast recuperation of the xenon with transfer rates exceeding 500 kg/hour in case of emergency.

	3.3.4.

  1, 83m Kr is an internal source of calibration used in XENONnT to study the detector response to electronic recoil at low energies and uniformly in the

	1/2 -J P	83m Kr	41.5 keV
	1.83 h	100% IC & Auger + X-ray
	7/2 +		9.4 keV
	156.8 ns	95% IC & Auger + X-ray 5 % 𝛾
	9/2 +	83 Kr	0 keV

whole LXe sensitive volume. In addition to its short half-life of 1.83 h, which allows for a quick restart of blinded data taking without being affected by residual radioactive contamination, the 83m Kr decay is characterized by two subsequent transitions at 32.1 keV and 9.4 keV, mostly from internal conversion (IC) as shown in figure 4.4. The 156.8 ns half-life of the intermediate level induces a particular signature of the 83m Kr calibration source. In comparison to the typical width of S1 and S2 signals, of O(100) ns and O(1) µs respectively, the intermediate half-life is such that the signal discrimination between the two decay steps by strax(en) is not always possible for S1s and extremely challenging for S2s.

Fig. 4.4 -Decay scheme of 83m Kr.

Figure reproduced from

Table 4 .

 4 4.2. 83m Kr Calibration and Signal CorrectionThis concludes the definition of the KrSingleS1 selection criteria, summarized below with the different boundaries for each variable discussed previously. For each cut, its acceptance (ratio between the number of events surviving the selection and number of events before applying the cuts) and total acceptance after applying all the cuts successively are summarized in table 4.1. 1: List of selection criteria defined to isolate the KrSingleS1 population. The corresponding acceptance of each cut as well as the total acceptance applying them successively is also provided.

	Selection Criteria: KrSingleS1 population
	• 110 < S1 a contributing PMTs < 250
	• S1 a max PMT area < 30 PE if z > -130 cm
	or S1 a max PMT area < 100 PE
	• 180 PE ≤ S2 a max PMT area < 1000 PE • 2500 PE ≤ S2 a area < 20000 PE • S2 b area < 60 PE
	• No S1 b
	Cut name	Cut acceptance [%] Total acceptance [%]
	Reconstructed events by strax(en) without any cuts	100.00	100.00
	Cut number of contributing PMTs to S1 a	90.08	90.08
	Cut area of the max PMT contributing to S1 a	98.51	88.75
	Cut area of the max PMT contributing to S2 a	97.14	86.20
	Cut S2s areas	77.45	66.77
	Cut no S1 b	77.36	51.66

Table 5 .

 5 1: characteristics of the WIMP and 0νββ decay searches in XENONnT.

	Physics Case	Standard WIMP search	0νββ decay search
	Signal	WIMP-Nucleus elastic scattering [NR] Summed electrons energies [ER]
	Energy ROI Dominant bakcground	O(10) keV Intrinsic backgrounds	Q ββ ∽ 2457 keV Materials backgrounds

  238 U early = 238 U → 230 Th 232 Th early = 232 Th → 228 Ac 238 U late = 226 Ra → 206 Pb 232 Th late = 228 Th → 208 Pb

	(5.4)
	MC simulation for each component and isotopes listed in table 5.2 were produced
	with O(10

8

-10 9 ) events statistics to exceed the expected exposure of XENONnT. A

2. Désintégration double beta et detection directe de Matière Noire

  topes, types d'interaction, gamme d'énergie, etc...) est intrinsèquement liée au processus physique recherché ainsi qu'à la manière dont ils sont mesurés dans le milieu de détection.Différentes technologies de détection peuvent être employées afin de mesurer les signaux de scintillation, d'ionisation et de chaleur produits par la déposition d'énergie induite par un processus physique dans le milieu de détection. Les technologies de détection les plus couramment utilisées dans les expériences de physique d'événements rares sont décrites plus en détails dans le chapitre 1. Chacune vise à mesurer l'un, ou une combinaison, des signaux produits et possède certaines forces et faiblesses (niveau de bruits de fond, taille de la masse cible, etc...). Dans le cas de l'expérience XENONnT, la technique de détection employée est celle de la chambre à projection temporelle (TPC) qui permet de mesurer les signaux de scintillation et d'ionisation et dont les caractéristiques sont discutées dans Ces deux types d'interactions peuvent donc être une source de bruit de fond en fonction du signal recherché, tel que c'est le cas pour la recherche de désintégration double beta et la détection directe de matière noire comme cela sera rappelé plus tard. Malgré l'existence des différents mécanismes d'interaction des neutrinos mentionnés précédemment, leurs faibles taux d'interaction rendent leur étude difficile. À ce jour, de nombreuses zones d'ombres subsistent dans notre compréhension de cette particule élémentaire, notamment sur l'origine de sa masse, sa nature (Dirac ou Majorana), et son rôle dans la genèse de l'Univers.Alors qu'initialement le neutrino avait été introduit dans le MS, en se basant sur des observations empiriques, comme étant une particule sans masse, l'observation en 1998 de l'oscillation de saveurs des neutrinos par l'expérience Super-Kamiokande a définitivement remis en question cette hypothèse. En effet, l'oscillation d'un neutrino produit initialement dans une saveur β vers une autre saveur α 2 , est un phénomène qui ne peut être expliqué que si les neutrinos ont une masse non nulle (démonstration dans le corps principal du manuscrit). Le formalisme décrivant ce processus permet de relier trois états de saveurs des neutrinos (ν e , ν µ , ν τ ) avec trois états de masse (ν 1 , ν 2 , ν 3 ), dont la relation est régie par la matrice de mélange PMNS (Pontecorvo-Maki-Nakagawa-Sakata). De nombreuses expériences ont été et continuent d'être menées pour étudier ce phénomène et mesurer avec la plus grande précision possible les paramètres de cette matrice de mélange, à savoir les angles de mélange θ 12 , θ 13 et θ 23 , le terme de phase de violation de la symétrie Charge-Parité (CP) δ CP et les différences de masse au carré ∆m2 21 et ∆m2 31 . Malheureusement, ces expériences ne sont sensibles qu'aux différences de masse au carré, et ne peuvent

	la section A.3.
	Selon le processus physique d'intérêt, certaines catégories de détecteurs seront plus
	adaptées que d'autres. Par conséquent, une compréhension approfondie de ce processus
	est nécessaire pour comprendre le choix de la technique de détection. Ce sujet est abordé
	dans la section suivante.
	Dans le domaine de la physique d'événements rares, deux noms emblématiques viennent
	à l'esprit instinctivement: les neutrinos et la Matière Noire.
	Dans le Modèle Standard (MS) de la physique des particules, théorie décrivant les
	particules élémentaires composant notre Univers ainsi que leurs interactions fondamen-
	tales à l'exception de la gravitation, le neutrino tient une place très particulière. Les neutrinos sont des leptons, particules élémentaires ayant un spin 1/2, neutres qui inter-agissent uniquement via l'interaction faible. Il existe trois saveurs différentes de neutrinos, le neutrino électronique (ν e ), muonique (ν µ ) et tauique (ν τ ), associées aux trois leptons chargés correspondant, l'électron (e -), le muon (µ -) et le tau (τ -), qui eux interagissent via l'interaction faible et électromagnétique. De par leur nature neutre, les neutrinos interagissent très rarement avec la matière. Deux catégories d'interactions entre les neu-trinos et les autres fermions existent, l'interaction par courant neutre (Neutral Current -NC) et par courant chargé (CC), impliquant respectivement l'échange d'un boson (par-ticules vectrices des interactions fondamentales) W ± ou Z 0 . De nombreux mécanismes d'interactions des neutrinos existent via les courants neutres et chargés, dépendant de la saveur et de l'énergie du neutrino. Deux mécanismes d'interactions à faibles énergies (inférieures à 100 MeV) des neutrinos avec la matière, d'intérêt pour la compréhension du reste de cette thèse méritent d'être mentionnés : la diffusion élastique neutrino-électron et la diffusion élastique cohérente neutrino-noyau. Ces deux processus sont décrits plus en détail dans le corps principal du manuscrit, concluant que l'information importante à retenir est que la diffusion élastique neutrino-électron induit un recul électronique tandis que la diffusion élastique cohérente neutrino-noyau induit un recul nucléaire de l'atome 31 > ∆m 2 21 ou cible. donc que renseigner la hiérarchie de masse des neutrinos (ordre normal ∆m 2 inversé ∆m 2 31 < ∆m 2 21

A.

  1)La non-émission de neutrino implique une différence notable dans la cinématique du processus. L'énergie totale de la désintégration, notée Q ββ (de l'ordre du MeV pour ce type de réaction), est répartie entre le noyau fils et les deux électrons émis, alors que dans le cas de la désintégration 2νββ , la répartition de l'énergie totale inclut aussi les deux neutrinos. Cela implique un spectre en énergie pour les deux électrons émis continu pour la désintégration 2νββ et un spectre en énergie discret centré au niveau de l'énergie totale disponible pour la désintégration 0νββ . C'est cette différence entre la distribution en énergie des deux électrons émis qui constitue la signature caractéristique de la désintégration 0νββ qui est recherchée par les expériences dédiées. À ce jour, la désintégration 0νββ n'a pas encore été observée, mais des limites sur la demi-vie du processus ont été établies pour les différents noyaux étudiés. On peut notamment mentionner l'isotope du136 Xe qui

est l'un des plus prometteurs et d'intérêt pour cette thèse car naturellement présent dans l'expérience XENONnT. La limite actuelle sur la demi-vie de la désintégration 0νββ de l'isotope

136

Xe est fixée à T 0ν 1/2 > 2.3 × 10 26 années par l'expérience KamLAND-Zen.

•

  Le xénon liquide (LXe) naturel utilisé dans XENONnT est le gaz noble le plus radiopur. Il ne contient que deux isotopes radioactifs : le 124 Xe et le 136 Xe, qui subissent une double désintégration faible. Cette composition naturellement radiopure est un atout majeur pour les recherches d'événements rares.

	• Deux types d'interactions peuvent se produire dans le xénon liquide, les reculs élec-
	troniques (ER) et les reculs nucléaires (NR). Les interactions électroniques sont
	induites par des particules chargées ou des neutrinos électroniques, et les interac-
	tions nucléaires sont induites par des particules neutres et/ou massives, telles que les
	neutrons, les neutrinos, ou bien les WIMPs. Au travers des processus d'ionisation
	et d'excitation du xénon, liés par un processus de recombinaison décrit plus en
	détail dans le corps du manuscrit, il est possible de différencier ces deux types
	d'interactions. En effet, la quantité de quanta de charge produite par un ER est
	plus importante (pour une même énergie déposée) que pour un NR, du fait d'une

• Le xénon possédant un numéro atomique élevé (Z = 54) et une densité élevée à l'état liquide (ρ LXe = 2.862 g/cm 3 à 177 K), il offre une capacité de blindage élevée contre les sources de bruits de fond extérieurs. De plus, avoir une densité élevée a pour autre avantage de permettre la construction de détecteurs compacts avec de grandes masses cibles. • Les propriétés de scintillation et d'ionisation du xénon, lorsqu'une particule y interagit et dépose de l'énergie, permettent également de l'utiliser comme milieu de détection. En tant que gaz noble, le xénon est transparent à sa propre lumière de scintillation. plus forte densité d'ionisation d'un électron. Les TPC à double phase au xénon peuvent mesurer à la fois la lumière et la charge produites et utiliser leur ratio pour distinguer les interactions ER et NR.

Le principe de fonctionnement d'une chambre à projection temporelle bi- phasée repose

  sur l'observation des signaux de scintillation et d'ionisation produite lors de l'interaction d'une particule dans la phase liquide. Dans le cas de XENONnT, il s'agit d'une TPC cylindrique remplie de xénon liquide avec une couche de xénon gazeux dans la partie supérieure. Lorsqu'une particule interagit dans la phase liquide, un signal de scintillation rapide (S1) est émis. Simultanément des électrons sont produits au niveau du point d'interaction, une partie de ces électrons va contribuer au signal S1 via le processus de recombinaison tandis que le reste va dériver vers le haut de la TPC sous l'influence d'un champ électrique (champ de dérive) appliqué dans le détecteur. Une fois arrivé à proximité de l'interface liquide/gaz du xénon, un second champ électrique (champ d'extraction) va accélérer les électrons pour les extraire dans la phase gazeuse où ils vont produire un signal d'électroluminescence (S2) proportionnel à la quantité de charge. La mesure des signaux S1 et S2 se fait à l'aide de deux réseaux de tube photomultiplicateur (PMT) placés aux extrémités supérieure et inférieure de la TPC. L'une des forces des TPC bi-phasées par rapport aux TPC mono-phasées est cette étape d'amplification du signal d'ionisation dans la phase gazeuse qui abaisse le seuil en énergie du détecteur. Il est possible, moyennant une compréhension suffisante de la réponse du détecteur via un étalonnage, de déduire Le design de l'expérience XENONnT est dans la continuité de son prédécesseur XENON1T. Une grande partie des infrastructures et des différents sous-systèmes nécessaires au fonctionnement du détecteur qui avaient été développés pour XENON1T sont réutilisés 6 . Cependant, plusieurs ajouts et améliorations notables ont été apportées au design de XENONnT afin d'augmenter la sensibilité du détecteur pour la recherche de MN et de la désintégration 0νββ . Par la suite nous présenterons rapidement les nouveaux éléments majeurs de l'expérience XENONnT, tandis qu'une description plus complète est offerte dans le corps du manuscrit.• La chambre à projection temporelle de XENONnT, ayant pour dimensions 161.3 cm de hauteur et 132.7cm de diamètre, possède un volume ∼ 3 fois plus grand que XENON1T permettant de contenir 5.9 tonnes de xénon. Le volume sensible de la TPC est délimité sur les côtés par une structure cylindrique en polytetrafluoroethylene (PTFE), offrant une haute réflectivité de la lumière de scintillation émise par le xénon. Les champs de dérive et d'extraction sont produits par le biais de 5 électrodes à fil exhibant une forte transparence (> 95%) afin de perdre le moins de lumière possible. La cathode et la grille, responsables du champ de dérive, se situent dans la phase liquide au fond de la TPC et à proximité de l'interface liquide-gaz du xénon, délimitant respectivement les limites supérieure et inférieure du volume sensible. Le champ d'extraction est appliqué entre la grille et l'anode, situé dans la phase gazeuse. Les deux dernières électrodes, situées au-dessus de l'anode (électrode-écran du haut) et sous la cathode (électrode-écran du bas), servent à protéger les deux réseaux de PMTs de la TPC. Ces réseaux représentent les yeux du détecteur, situés en haut (bas) de la TPC et se composent de 253 (241) 3" Hamamatsu R11410-21 PMT, optimisés pour capter la longueur d'onde de la lumière de scintillation émise par le xénon à 178 nm. En effet la présence d'impureté dans le xénon peut engendrer l'absorption d'une partie de la lumière de scintillation et la capture de certains électrons dérivant vers la phase gazeuse. Cela induisant une atténuation des signaux S1 et S2 observés pouvant limiter l'efficacité de détection des dépôts de faible énergie. De plus certains éléments contaminants la cible de xénon peuvent être radioactifs et donc une source de bruit de fond. Le premier nouveau système visant à améliorer le niveau de pureté du xénon est un système de purification liquide ayant pour objectifs la suppression des impuretés électro-négatives. Le second système est une nouvelle colonne de distillation développées afin de séparer l'isotope de 222 Rn, source de bruit de fond majeur pour la recherche de MN, continuellement introduit dans la cible de xénon par émanation des matériaux du détecteur. Ces nouveaux systèmes ont permis d'atteindre un niveau de pureté de la cible de xénon inégalé jusqu'ici.

	Cette enceinte d'un diamètre de 9.6 m et d'une hauteur de 10.2 m, est instrumen-
	tée de 84 Hamamatsu R5912ASSY 8" PMTs afin d'être utilisée comme détecteur à
	muons (système de veto). En plus de ce système de veto à muons, un second sys-
	tème de veto a été installé pour XENONnT. Celui-ci consiste en un second volume
	de détection construit dans le veto à muons et entourant le cryostat contenant la
	TPC. Ce nouveau volume est isolé optiquement du reste de l'enceinte d'eau et est
	instrumenté par un réseau de 120 Hamamatsu R5912-100-10 8" PMTs. Ce nouveau
	volume a pour objectifs d'identifier la présence de neutrons (veto à neutrons), l'une
	des sources de bruit de fond pour la recherche de MN. Au moment de la rédaction
	de cette thèse, l'enceinte en acier contenant les systèmes de veto à muon et neutron
	est remplie d'eau pure, mais à terme l'eau sera dopée avec du sel de Gadolinium afin
	d'améliorer l'efficacité de détection des neutrons dans le système de veto à neutron.
	Cette efficacité de détection des neutrons est estimée à ∼ 68 % avec de l'eau pure et ∼ 87 % avec le Gadolinium.

certaines propriétés de l'interaction initiale via la mesure des signaux S1 et S2: La position du point d'interaction en trois dimensions, la profondeur étant donnée par le temps de dérive des électrons (différence de temps entre le signal S1 et S2), tandis que la position dans le plan (x, y) est reconstruite via le motif de lumière mesuré par le réseau de PMTs situé en haut de la TPC. La multiplicité de l'événement, c'est à dire le nombre d'interactions ayant eu lieu dans la TPC, peut être déterminée par le nombre de signaux S2 observés. Le type d'interaction (ER ou NR) ayant produit ces signaux peut être discriminé par le ratio des amplitudes des signaux S2 et S1, comme expliqué précédemment. Enfin, L'énergie déposée lors de l'interaction peut être reconstruite via la conversion des signaux S1 et S2 en quantité de lumière et de charge produite initialement. • Les systèmes de blindages passifs et actifs successifs ont été mis en place afin de protéger la TPC des sources de bruit de fond externes. La TPC est placée au cur d'un cryostat en acier à double paroi isolé par du vide, lui-même situé au centre d'une enceinte d'acier remplie d'eau qui avait été construite pour XENON1T. • Deux nouveaux systèmes de purification et distillation ont été installés afin d'améliorer le niveau de pureté de la cible de xénon qui est un enjeu majeur pour les performances du détecteur. • Le système d'acquisition de données (DAQ) a été amélioré afin de pouvoir gérer l'augmentation du nombre de PMTs (TPC, veto à muons et neutrons), ainsi que d'introduire une nouvelle logique d'acquisition de données sans système de déclenchement physique. • Un nouveau système de récupération et de stockage du xénon (ReStoX 2) a dû être construit afin de prendre en compte l'augmentation de la quantité de xénon utilisée dans l'expérience (8.3 tonnes au total). Ce nouveau système, une enceinte cylindrique en acier à double paroi isolée par du vide, permet une récupération rapide du xénon avec un débit de 500 kg/heure en cas d'urgence et une capacité de stockage de 10 tonnes de xénon à température ambiante. Ce nouveau système est l'une des contributions majeures du CNRS pour l'expérience XENONnT.

  222 Rn, présent dans la cible de xénon par émanation continue depuis les matériaux du détecteur, le214 Bi est une source de bruit de fond pour la recherche de désintégration 0νββ . Il se désintègre en214 Po par émission β avec une énergie maximale disponible à 3269 keV, bien au-dessus de Q ββ , et une demi-vie de 19.8 minutes. Dans 19.1% des cas, le214 Po est produit à l'état fondamental sans émission de γ, ce qu'on appelle le "naked-β". Dans les 80.9% restants, la désintégration β est suivie de rayonnements γ, dont la ligne la plus problématique se situe à 2447.9 keV. La désintégration β du214 Bi vers le214 Po est rapidement suivie de l'émission α de ce dernier pour former le210 Pb, avec une demi-vie de 162.3 µs. Cela conduit à une topologie particulière d'événement qui peut être facilement identifiée et rejetée si les désintégrations β et α sont détectées dans le volume actif du TPC. Cette technique, appelée BiPo tagging, a une efficacité estimée à 99.8 %. Cependant la technique du BiPo tagging ne peut pas être appliquée aux désintégrations du 214 Bi se produisant dans la partie non instrumentée entourant la paroi en PTFE de la TPC, car l'α peut échapper à la détection. Dans ce cas, le rayonnement γ de haute énergie émis par le 214 Po peut atteindre le volume fiducial (FV) et imiter la signature d'une désintégration 0νββ . Cela implique que les deux contributions provenant de la désintégration du 214 Bi dans le volume actif et dans la partie noninstrumentée du LXe doivent être modélisées séparément.• Bruit de fond interne: la désintégration 2νββ du 136 Xe, partageant la même Q ββ que la désintégration 0νββ , est une source de bruit de fond naturelle pour cette dernière. En raison de la résolution en énergie du détecteur, le spectre en énergie reconstruit de la 2νββ peut se terminer à des énergies supérieures à Q ββ . Une mod-A.5. Estimation de la sensibilité de XENONnT pour la recherche de désintégration double beta sans émission de neutrino du 136 Xe élisation précise de ce spectre via simulation MC peut s'avérer difficile, notamment au niveau de la queue de la distribution qui décroît rapidement. Il peut être très coûteux en termes de temps de calcul de simuler un grand nombre d'événements de 2νββ afin de modéliser avec précision la queue de la distribution, qui correspond à la partie tombant dans la région d'intérêt de la 0νββ . Afin de modéliser avec précision la désintégration 2νββ du 136 Xe, un spectre théorique de la somme des énergies des deux électrons émis a été utilisé, permettant de contourner ce problème de statistiques. Des simulations MC (avec DECAY0) ont toutefois été utilisées afin de paramétriser la réponse du détecteur (notamment le pouvoir de séparation) et l'appliquer au spectre théorique. • Diffusion élastique neutrino-électron induite par les neutrinos solaires du 8 B. L'énergie des neutrinos électroniques, produits lors des désintégrations β du 8 B au cur du soleil, peut atteindre 15 MeV. Ils peuvent interagir avec les électrons du milieu, via diffusion élastique, et produire des reculs d'électrons d'énergie pouvant aller jusqu'à O(10) MeV. Du fait de leur énergie, ils peuvent être confondus avec des événements de désintégration 0νββ . Afin de modéliser cette source de bruit de fond, il est nécessaire d'estimer le taux d'interaction attendu de la part des neutrinos solaires du

The exposure is the product of the target mass and livetime of the experiment.

Theory describing how all known elementary particles, building blocks of our universe, and three of the four known fundamental forces (electromagnetic, weak, and strong[START_REF] Sheldon | Partial-symmetries of weak interactions[END_REF][START_REF] Weinberg | A model of leptons[END_REF][START_REF] Salam | Weak and electromagnetic interactions[END_REF].) are related to each other.

Like the nature of neutrino, or the ordering of their mass hierarchy. Those notion will be introduce in section 2.1.2.

It was actually the first detection of an electron anti-neutrino.

The gravitational force is described by the general relativity which is not part of the SM.

Low momentum transfer, imply small de Broglie wavelegnth compare to the size of the nucleus, leading to a coherent enhancement of the interaction cross-section.

Neutrino are Majorana particles if they are their own anti-particles. This notion will be introduced later on.

Produced through nuclear reaction occurring in the heart of the Sun.

A proton beam is send towards a target, producing a large amount of π ± , that will later on decay through the π ± → µ ± + ν µ /ν µ reaction, resulting in a large amount of neutrinos.

It is not the only approach used to investigate the Majorana nature of the neutrino, accelerator experiment such as CMS[START_REF] Khachatryan | Search for heavy majorana neutrinos in e ± e ± + jets and e ± µ ± + jets events in proton-proton collisions at √ s = 8 TeV[END_REF] are also trying to probe the neutrino nature.

Where the parameters a i (i = v, s, c, a, p) refers to the volume, surface, Coulomb repulsion, asym-

The reader can refer to the following review[START_REF] Bilenky | Neutrinoless double-beta decay: A probe of physics beyond the standard model[END_REF] for a more general description of the other mechanisms not mentioned in this thesis.

[START_REF] Aghanim | results[END_REF] m light = m 1 in case of NO and m light = m 3 in case of IO.

See review from G. Bertone and D. Hooper for a complete description of the history of Dark Matter[START_REF] Bertone | History of dark matter[END_REF].

The gas clouds, dominant ordinary matter constituent of galactic clusters, collide and produce de-

The Λ refers to the cosmological constant necessary to explain the current accelerated expansion of the Universe.

Considering Summer and Winter seasons in the North hemisphere.

In biexcitonic quenching two excitons are quenched before the excited molecular states are formed. In Penning quenching, two excited molecular states collide to produce one excited state, and one of the states dissociates to the ground state[START_REF] Hogenbirk | Precision measurements of the scintillation pulse shape for low-energy recoils in liquid xenon[END_REF].

Like multiples neutron scattering for WIMP search, or multiple compton scattering from high-energy gamma for 0νββ search.

Straxen is the analysis framework for XENONnT, built on top of the generic strax framework.

For example, the information on the number of hits seen by each PMTs for each peak is not saved at the event levels, to save memory usage.

Light reflection on the PTFE walls and lower PMTs coverage, make the position reconstruction more challenging.

The FV used is the one optimised for the low energy ER search[START_REF] Aprile | Search for new physics in electronic recoil data from XENONnT[END_REF].

This is due to its refractive index of ∼ 1.57[START_REF] Barkov | Measurement of the refractive index of liquid xenon for intrinsic scintillation light[END_REF].

Defined as the measured amount of light (S1) per deposited energy.

Such as the start of the Rn distillation column, or changes in the xenon purification circuit, necessary for the tritium enhanced periods at the end of SR0.

To measure the CYs at 32.1 keV and 9.4 keV using the methodology described in the previous paragraph, it would have been needed to reconstruct the two S2s separately. This would have been possible by selecting the KrDoubleS1DoubleS2 population introduced in section 4.2.1, that instead was not possible to isolate in SR0.

The fit do not start at 400 ns to exclude the transition region between events not separated by strax(en) and the KrDoubleS1 population, visible in figure4.[START_REF] Aker | Direct neutrino-mass measurement with sub-electronvolt sensitivity[END_REF]

The LY and CY are different between an α, γ, and β, due to a different ionization density.

Q value of the[START_REF] Bolton | Two-neutrino double beta decay with sterile neutrinos[END_REF] Xe 0νββ decay at

2457.8 ± 0.4 keV[START_REF] Redshaw | Mass and double-beta-decay q value of 136 Xe[END_REF].

Position reconstruction algorithms used in XENONnT are presented in section 4.1.

γ-screening performed with several highly sensitive germanium spectrometers.

It was not applied for the[START_REF] Browne | Nuclear data sheets for A = 60[END_REF] U decay chain due to its negligible contamination in detector materials[START_REF] Aprile | Material radiopurity control in the XENONnT experiment[END_REF].

To be sure to not miss any events, and therfore decay chain step, in the non instrumented LXe.

where the number of bins is chosen to contain at least 10 simulated events in each bin

This number of events allowed a modelization of the whole spectrum with sufficient statistics and a reasonable computational time (1 day).

A similar order of magnitude were observed in XENON1T, and no measurement was available for XENONnT at the time of the study.

Generate a "perfect dataset" considering the median background model without fluctuations.

Les indices β et α peuvent prendre n'importe quelle valeur entre électronique, muonique et tauique.

Les neutrinos sont de Majorana s'ils sont leurs propres antiparticules. La désintégration double bêta sans émissions de neutrinos n'est possible que si le neutrino est une particule de Majorana.

Par soucis de simplicité et de lisibilité, dans la suite du texte, les désintégrations double-β -avec et sans émission de neutrino seront référées respectivement par les notations 2νββ et 0νββ .

Induit par la rotation de la terre autour du soleil et du soleil autour du centre galactique.

Certains éléments de XENON1T avaient été conçus en prévoyant la mise à niveau vers XENONnT

Acknowledgments

J'écris, non sans émotion, les dernières lignes de cette thèse, clôturant ainsi une étape importante de ma vie. Ce fut une expérience unique, une aventure incroyable, avec de belles rencontres et des moments de profonde introspection (#COVID). Il y a eu des hauts et des bas, des défis et des succès, mais une certitude subsiste : il y a un avant et un après thèse et j'en ressors grandi. Évidemment, tout cela aurait été impossible seul, et j'aimerais pouvoir remercier toutes les personnes qui m'ont accompagné ces trois dernières années lors de ce périple. Mais il y en a tellement qu'il faudrait que je rédige une thèse à ce sujet et j'avoue que là, tout de suite, je ne suis pas trop partant. Je vais malgré tout essayer. Je ne suis pas très bon pour les remerciements à l'écrit, je ne suis pas un grand écrivain (je n'ai pas la plume de Robin Hobb), mais je vais faire de mon mieux.

First of all, I would like to thank the two reviewers of my thesis, Alessandra Tonazzo, and Fabrice Piquemal, for agreeing to dedicate some of their time to read my manuscript and provide very constructive comments and suggestions. I would also like to thank the other members of my committee, Laura Baudis, and Pol-Bernard Gossiaux, for their interest in my work and their implications during my defense. A thought for Elisabetta Barberio, who unfortunately was not able to attend the defense, but with which I had really enlightening discussions during my thesis as she was part of my CSI.

Je tiens à remercier mon directeur de thèse, Dominique Thers, d'avoir eu confiance en moi en m'acceptant pour cette thèse au sein du groupe Xenon. Je suis reconnaissant pour les nombreuses discussions que nous avons eues, toujours enrichissantes même si la digression était souvent au rendez-vous. Merci pour tes conseils et ton soutien constant au cours de ces dernières années.

Je ne saurais comment exprimer pleinement ma gratitude envers mon encadrante, Sara Diglio, sans qui cette thèse n'aurait pas été aussi enrichissante. Merci infiniment pour tes conseils, ton implication constante, ton soutien indéfectible, ta bienveillance, ta pédagogie et ta patience, notamment lors de la rédaction. Et la liste est encore longue. Merci pour tout. Ce fut un honneur et un véritable plaisir de t'avoir eue comme encadrante.

Merci infiniment au reste du groupe Xenon que j'ai pu côtoyer : Julien, Eric, Mariangela, Pascal, Nicolas, Yajing, Yue, Chloe, Clotilde, Marina, Johan, Dingbang, Lorenzo, Evgenii, Paco. Ce fut un plaisir de travailler avec vous et de partager ces moments de convivialité lors de ces trois dernières années. Une pensée particulière pour Jean-Pierre qui

Internal background

238 U. This background can be efficiently shielded by the Water Tank (WT), which offers a reduction factor of O (10 6 ) per meter of water on the neutron flux [START_REF] Selvi | Study of the performances of the shield and muon veto of the XENON1T experiment[END_REF].

• Neutrons from natural radioactivity in the materials of the detector: originating from the U and Th decay chains present in the materials of our detector, they cannot be completely shielded by the WT and are therefore more dangerous.

We used the radiogenic neutron simulations in the materials from the XENONnT WIMP projection study to estimate the 137 Xe production rate induced by this source in the TPC. We found a value of 4 × 10 -8 isotope/kg/year for 137 Xe, which is negligible compared to the last source of neutrons of this list.

• Muon-induced neutrons in the cavern: Similar to neutrons from natural radioactivity in the cavern, muon-induced neutrons in the cavern can be efficiently shielded by the water tank [START_REF] Selvi | Study of the performances of the shield and muon veto of the XENON1T experiment[END_REF].

• Muon-induced neutrons in the materials of the detector: These neutrons are the main contributors to the production of 137 Xe in the TPC. The contribution from muon-induced neutrons in the materials is more significant than that from natural radioactivity, as shown in the next section.

Figure 5.12 shows that it is possible to distinguish several parts of the experiment where 137 Xe can be produced and classify them in two categories:

• Sub-system shielded by the WT. The TPC itself, where the only neutron source sub-system to go back into the TPC, that was estimated to be ∼ 30 sec. Due to the slow flow of xenon circulating in the Rn distillation column, its contribution is negligible to the other purification systems or the TPC. The LXe purification loop contribute at more than 90% to the total 137 Xe production rate A total 137 Xe . Now we have access to all the information necessary to build the background model from 137 Xe β-decay from MC simulation.

137 Xe Background model

A large sample of 137 Xe events, O(10 8 ) 12 , were simulated via our GEANT4 framework with a homogeneous distribution in the whole LXe volume. The full 137 Xe decay chain, described in figure 5.11, was simulated and led to a weighting factor W i value of 2.947±0.2 for the mean length of the decay chain in GEANT4. Figure 5.16 shows the expected energy spectrum from 137 Xe decay derived from the MC framework describe in section 5.1, with its associated uncertainty estimated to be close 70% near the Q ββ . This spectrum will be used as a background model for 137 Xe decay. For comparison purposes, the material background spectrum is also shown. We can clearly state that, despite our conservative scenario that provides an upper limit on the 137 Xe production rate, the background from materials is still the dominant one. 214 Bi induced by 222 Rn emanation As introduced in section 3.3.3, continuous contamination of the xenon target is introduced via all the materials in contact with xenon due to the emanation of Radon. It induce a second contribution from the 238 U primordial decay chain products to the one from materials. Among the daughter nuclei of the 222 Rn decay chain, shown in figure 5.6, the only relevant one for 0νββ decay search is 214 Bi. It decays to 214 Po via β emission with a Q-value at 3269 keV far above Q ββ and a half-life of 19.8 minutes. In 19.1% of cases, the 5.6. Sensitivity projection results Table 5.5: List of all parameters in the fit of the projection study along with their units and Gaussian constraint terms and a summary of the expected background events in the 2σ E range around Q ββ for 1000 days of live time and an FV mass of 1088 kg. The constraint terms are given relative to the nominal value and stem from material screening measurements [START_REF] Aprile | Material radiopurity control in the XENONnT experiment[END_REF] for materials backgrounds or dedicated MC study for internal backgrounds. There are no energy depositions of 238 U and 232 Th in the ROI. Therefore, we do not give a number of expected events for these isotopes.

β-and γ-decay from

Parameter

Unit Constraint Expected Events

The resulting A 0νββ amplitude crossing the asymptotic threshold for a given livetime of the experiment can be converted into a lower limit on the half-life using:

Where N A is Avogadro's number, η 136 Xe the natural abundance of 136 Xe in our xenon target, M A = 0.131 kg.mol -1 is the xenon molar mass, and P SS = 0.91 is the fraction of signal events that are identified as SS events, derived in section 5.2.

Sensitivity projection results

For a live time of 1000 days, we obtain a median lower limit of:

1 × 10 25 yr at 90 % CL.

(5.27)

The four limits obtained from the set of experimental livetimes tested were interpolated with a square root function corresponding to the expected functional behavior for increasing livetimes. The result is shown in figure 5.26 with the projected (solid lines) and measured (dashed lines) from KamLAND-Zen and EXO-200 dedicated experiments but also XENON1T result for comparison purposes. This result is below the current best limit from KamLAND-Zen and EXO-200, mostly due to an extensive background contribution from the detector materials, which were selected to optimize the background level at low energy for WIMP search and not for 0νββ decay search. The SS cryostat is the main tions of LYs and CYs with respect to their means of < 1% and < 2%, respectively. It is worth mentioning that the analysis of SR0 data presented in this work was developed and optimized for searches at low energies, namely for nuclear recoils of WIMPs and for electronic recoil searches. Therefore, additional work to validate and improve the signal reconstruction and correction will be necessary in order to search for rare events at higher energy (O(1) µMeV), such as neutrinoless double beta decay of 136 Xe with XENONnT data.

Appendix A

Résumé en Français

Le propos de cette annexe est d'offrir un résumé en français des travaux de thèse, présentées dans le corps principal de ce manuscrit, portant sur la recherche de désintégration double beta sans émission de neutrino du 136 • Un événement rare est un signal induit par un processus physique spécifique se produisant rarement dans le milieu de détection utilisé pour l'observer et ayant une signature particulière.

• Un événement de bruit de fond est produit par un processus physique indésirable qui imite la signature du processus de l'événement rare recherché.

• La sensibilité, ou le potentiel de découverte, des expériences de recherche d'événements rares, est principalement définie par leur niveau de bruit de fond et le taux de signal attendu. Par conséquent, la compréhension des différentes sources de bruit de fond et la mise en place de stratégies afin de les atténuer sont essentielles pour la recherche de processus rares. Trois catégories principales de bruit de fond peuvent être identifiées, avec leurs stratégies de réduction associées :

• Les bruits de fond cosmogéniques, induits par les particules secondaires produites par l'interaction de rayons cosmiques avec l'atmosphère terrestre. Ce type de bruit de fond peut être efficacement réduit en opérant les expériences de physique d'événements rares dans des laboratoires souterrains. Une majorité des particules • Source interne de 83m Kr offrant deux conversions internes successives à 9.4 keV et 32.1 keV. Cette source de calibration est une pierre angulaire pour la caractérisation et la correction des effets du détecteur. La procédure de sélection de ces événements était l'une de mes responsabilités pendant SR0.

A.3. L'expérience XENONnT

• Source interne de 220 Rn permettant de caractériser la réponse du détecteur pour les ER grâce aux émissions β du 212 Pb qui offre un spectre relativement continu dans la gamme d'énergie de la recherche de MN.

• Source interne de 37 Ar dont les lignes mono-énergétiques à 0.27 keV et 2.8 keV permettent de valider la réponse du détecteur pour les ER à faibles énergies et