After the Big Bang matter and antimatter were present in equal amounts. Today, however, everything we see, is made almost entirely of matter. A fundamental ingredient to explain this asymmetry between matter and antimatter is the violation of the CP (Charge Parity) symmetry. CP violation has been observed but quantitatively not enough to explain the huge asymmetry. The Belle II experiment in Japan studies the particles produced in electronpositron collisions at the SuperKEKB collider, the highest intensity collider in the World, allowing a high precision measurements of the known sources of CP violation and looking for new ones. In this document, I present my work on measuring the CP violation in B meson radiative decays (decays with photon in final state) particularly promising thanks to their high sensitivity to possible new processes. Following this analysis, I present a new measurement of the B mesons lifetime where I could verify the robustness of the tools used in the CP violation measurement.

Thanks to all whom helped in contributing and finishing this work. My supervisor Jerome Baudot, thank you for all the ideas and instructions that helped me evolve my thesis with great results, thank you as well for all the humanistic care you gave me through my ups and downs during these three years. Isabelle-Ripp Baudot, thank you being the strong boss organizing all our activities in the Belle II collaboration, and a great co-director for my thesis. Special thanks for Giulio Dujany for this contribution to the B 0 lifetime analysis that helped to make it more complete

Introduction

The main subject of my PhD is to search for experimental signs of New Physics (NP) that cannot be described by the current theory of particle physics, the Standard Model (SM). There are several ways to look for NP. At colliders, these studies are carried with the large hadron collider (LHC) of the European Organization for Nuclear Research (CERN) and with superKEKB located at the High Energy Accelerator Research Organisation in Japan (KEK). The latter was build to create a clean environment using the e + e -collisions, to study NP mainly in B and D meson and τ lepton systems, while the LHC collider has a wider physics programs using pp collisions. The two previous projects of asymmetric B-factories, PEP-II [START_REF]PEP-II: An Asymmetric B Factory[END_REF] at SLAC and KEKB [START_REF] Oide | KEKB B-factory, the luminosity frontier[END_REF] at KEK started in 1999 and stopped in 2008 and 2010 respectively. The Belle experiment at KEK, recorded data at the world record instantaneous luminosity of 2.11 × 10 34 cm -2 s -1 . A major success of these B-factories was the experimental confirmation of the formalism for CP (charge parity) violation proposed by Kobayashi Makoto and Toshishide Maskawa, who won the physics Nobel prize in 2008 for the "discovery of the origin of the broken symmetry which predicts the existence of at least three families of quarks in nature".

Introduction

is their sensitivity to new particles since they involve b to s quark transitions through quantum loops. While the Standard Model almost forbids any CP violation in such decays, NP models could generate sizable violation by restoring to some level the Left-Right symmetry broken in the SM that predicts photons emitted in b → s γ decays are only left-handed, up to small corrections.

Hence in my PhD, I worked on the measurement of the indirect and direct CP violation parameters, S and C respectively, in the b → sγ transitions occurring in the two decays B 0 → K 0 s π + π -γ and B 0 → K 0 s π 0 γ as suggested in [START_REF] Atwood | Mixing induced CP asymmetries in radiative B decays in and beyond the standard model[END_REF]. The branching fractions of these channels are 7 × 10 -6 and 9.5 × 10 -6 respectively, which are relatively small. Measurements on these channels were done by Belle [START_REF] Ushiroda | Belle, Time-Dependent CP Asymmetries in B 0 → K 0 S π 0 γ transitions[END_REF] [START_REF] Li | Belle, Time-dependent CP Asymmetries in B 0 → K 0 S rho 0 γ Decays[END_REF] and Babar [START_REF] Aubert | Measurement of Time-Dependent CP Asymmetry in B 0 → K 0 S π 0 γ Decays[END_REF] [START_REF] Del Amo | BaBar, Time-dependent analysis of B 0 → K 0 S ππ + γ decays and studies of the K + ππ + system in B + → K + ππ + γ decays[END_REF] experiments. The statistically limited results did not yield positive outcome for the search of New Physics. My goal was to investigate the sensitivity in these channels to non-zero value of the indirect CP violation parameter S using "Time dependent CP violation", TDCPV analysis with the Belle II dataset.

I started to work using simulated data to setup and tune the analysis, which consists mainly in selecting events potentially corresponding to the channel and then perform a fit to the data in order to extract the CP-violating parameter S, finalizing the analysis, I evaluated the possible systematical uncertainties for both channels. In addition, I developed the first measurement of the B 0 lifetime with real data in Belle II, since B 0 lifetime is precisely measured in particle physics experiments, measuring it in Belle II is a first demonstration of the tools used for the TDCPV analysis. B 0 lifetime measurement was documented in a Belle II conference paper, reported in 2020 winter conferences and published in May 2020 [START_REF] Abudinén | Belle-II, Measurement of the B 0 lifetime using fully reconstructed hadronic decays in the 2019 Belle II dataset[END_REF]. Both, TDCPV and B 0 lifetime analysis are discussed in the present document that is organized as follow.

In chapter one, an overview of Standard Model is presented, charge and parity symmetries are introduced as well and the origin of the CP violation in the Standard Model is elaborated. Then the properties of the complex CKM matrix is examined in detail, formalizing quark-mixing being the origin of the CP violation. The triangle related to the B 0 d B 0 d system, where most exciting physics of CP violation lies, is examined with its sides and angles parameters as well the current experimental status of these parameters are summarized.

In chapter two, I present the quantum mechanical properties of the neutral B 0 meson and its phenomenology allowing for the extraction of various CP-violating quantities. After that, I introduce the CP violation in b → s γ transitions, its correlation with New Physics as well as the physical quantities used to probe a sign of NP. A summary of previous experimental results done using b → s γ transition channels used in this thesis closes the chapter.

Chapter three describes the B factory concept and the main upgrades Introduction needed to achieve the SuperKEKB designed luminosity of 8 × 10 35 cm -2 s -1 , 40 times higher than its predecessor KEKB. It also presents the main phases of the accelerator commissioning and its luminosity run plan, which is crucial for the data taking and physics reach of the Belle II program, then the detector is discussed in detail. In particular, I summarize the improvements with respect to Belle needed to meet the high luminosity requirements, and briefly describe the sub-detectors, the trigger system, and the software framework relevant for this analysis. TDCPV analysis strategy is fully detailed in chapter five. I start with the principles of this measurement and explain the tools, concepts used in the analysis. I elaborate the methodology followed to measure the CP violation parameters. Then, I list the results and explain the steps followed in the two analysis parts I studied for both channels, cuts optimization and systematical uncertainties calculation. I discuss the prospects of this analysis on the Belle II full data set, considering several improvement factors related to the fully installed detector and the increased luminosity.

Chapter six deals with the very first measurement of the B 0 lifetime with the real data accumulated in the first year of Belle II. The analysis is prepared on simulated samples with control data whenever possible. We especially insist on the development of the time resolution function, which is a crucial tool also for TDCPV analysis. Then the analysis method is applied blindly on the data to obtain the lifetime estimate and compared to the known world average value in order to assess the method robustness.

In the conclusion I summarize my results on the two aspects of my work, the TDCPV analysis preparation for radiative B decays and the early B 0 lifetime measurement and discuss the future prospects for both these analysis in Belle II.

CHAPTER 1

Overview of the Standard Model

In this chapter, I start with an overview of the Standard Model, then I introduce the charge and parity symmetries related to the main subject of this thesis, I elaborate the origin of the CP violation, the complex nature of the CKM matrix that is examined in detail, giving the relation between its elements and properties with CP violation of B d system. Finalizing with the current experimental status of CKM parameters. The Standard Model is a quantum field theory (QFT) that describes the dynamics of the known elementary particles, driven by the electromagnetic, weak and strong interactions. These interactions are mediated by the exchange of virtual particles, called gauge bosons. All gauge bosons included in the SM are vector bosons: they have a spin equal to 1 and obey Bose-Einstein statistics. Table 1.1 presents a list of SM interactions and their mediators (bosons). Although the gravitational force is not accounted for in the SM, its intensity at the elementary scale is so weak compared to the other interactions (many orders of magnitude lower) that it can be neglected. Finally, one should consider an additional fundamental particle: the recently discovered Higgs boson, a scalar boson of spin 0 associated with the so-called Brout-Englert-Higgs mechanism, through which the W ± and Z 0 gauge bosons and all elementary fermions acquire their masses.

In opposition to bosons, the fermions, which are the constituents of matter, The six flavours of leptons are grouped in three separate generations, composed respectively of the electron (e), muon (µ) and tau ( τ) leptons, and the corresponding neutral neutrinos ( ν e , ν µ , ν τ ). Charged leptons are sensitive to the electromagnetic and weak interactions, and have an integer electric charge of -1. Neutrinos only interact via the weak force and are considered massless in the SM, although it was proven experimentally that their masses must be extremely small but non-zero. Thus they interact very weakly and can only be detected with dedicated experiments. Quarks also come in 6 different flavours and are organized in three generations, comprising respectively the up (u) and down (d) quarks, the charm (c) and strange (s) quarks, and the top (t) and bottom (b) quarks. They are sensitive to the three interactions included in the SM, and they have a fractional electric charge of either + 2 3 or - 1 3 . Due to the particular behaviour of the strong force, quarks can not exist freely but only confined together into composite hadrons, such as protons and neutrons.

All fermions also exist as antiparticles, which are identical to their corresponding particles in every aspect except having opposite internal quantum numbers (such as the electric charge). For both leptons and quarks, the three generations are ordered by increasing mass, and particles of higher generations will decay into lower mass ones. For this reason, the three first-generation particles only make up all the ordinary matter: up and down quarks bound into protons and neutrons which form the atoms's nuclei, around which electrons orbit (in the semi-classic formalism). Figure 1.1 summarizes all the particles included in the SM and their categorizations.

Mathematically, the SM theory is a unified quantum field theory obeying the following gauge group symmetry SU (3)

C × SU(2) L × U(1) Y .
The interactions of quarks and leptons with the photon are described by the theory of quantum electrodynamics (QED) which is based on the Abelian, i.e. commutative, symmetry group of unitary 1 × 1 operators called U(1) EM , EM sands for electromagnetic. Strong interactions are described by quantum chromodynamics (QCD) which is based on the non-Abelian symmetry group SU(3) c . The subscript c stands for color charge, or just color, which is the quantum number corresponding to the charge of the interaction. The three degrees of freedom of the symmetry group are the degrees of freedom of the color charge, which are labeled in analogy to the three kinds of colors humans perceive: red, green, blue. Apart from electric charge, every quark carries one of the three different color charges. Bound states of quarks can only exist if they are colourless; e.g. if a meson contains a green quark, its antiquark must be antigreen. The fact that colored objects do not exist as free particles is called color confinement.

Considering now weak interactions, they differ from the electromagnetic and the strong interactions. The symmetry group of the weak interaction is the non-Abelian SU(2) L group, where the subscript L stays for left-handed, indicating that the fermions participating in weak interactions are left-handed. Lefthanded fermions form so-called weak isospin doublets and two such doublets compose each generation, while right-handed fermions are weak isospin singlet. The W ± and Z 0 bosons results from the unification of electromagnetic and weak interactions. The unified interaction is called electroweak interaction and is described by the electroweak theory which is based on the symmetry group SU(2) L U(1) Y , where the subscript Y stays for hypercharge. I moved this sentence at the end, where it has more impact. The charged mediators of the weak interaction, the W ± bosons, couple to all quark and lepton doublets; they are the only gauge bosons in the SM that can change the flavor of particles and are therefore responsible for most of the particle decays.

The mechanism providing mass to particles in the SM is implemented through the spontaneous symmetry breaking introduced by the Higgs complex scalar field, which has a non-zero vacuum expectation value and generates the masses of the gauge vector bosons (W + , W -, Z 0 ) and all the fermions except neutrinos in the model [START_REF] Bernstein | Spontaneous symmetry breaking, gauge theories, the higgs mechanism and all that[END_REF]. This ultimate piece of the standard model, the Higgs boson, was discovered in 2012 by the ATLAS and the CMS collaborations [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]. However, there are several open questions suggesting that the SM cannot be the ultimate theory. These theoretical and observational issues do not represent inconsistencies or direct violation of SM, hence they do not point clearly to some other theory. Finding the first indications for New Physics (NP) beyond the SM is the main goal of particle physics today. To search for such indications, there are two complementary approaches, the first one are direct searches for new non-SM particles, an approach that has been successful since the invention of colliders. The second one is indirect searches for non-SM effects by comparing precise measurements with precise SM predictions. Indirect searches focuses on processes where new particles can contribute as virtual particles. In this field quark flavor dynamics offers a large variety and abundance of processes that is sensitive to non-SM dynamics. Thus, offering the most promising opportunities for indirect searches. This thesis targets at making an essential contribution to the indirect searches at Belle II and is focused on the flavor dynamics of B mesons, in particular, on the phenomena related to the violation of the discrete charge-parity (CP) symmetry in this system.

Symmetries

Symmetries are fundamental in physics. They give rise to conservation laws, structure the formalism of theories and play a major role in our understanding of particle physics. A symmetry exists when a physical law is invariant under certain transformations. There are two types of transformations: continuous transformations, such as rotations or translations, and discrete transformations such as reflections or charge conjugations. The main subject of the thesis is related to two discrete symmetries, parity P and charge conjugation C, that are of fundamental importance in modern physics and defined as:

1. The parity transformation P defined as an inversion of the spatial coordinates at the origin, i.e (x, y, z) → (-x, -y, -z)

2. The charge conjugation C transforms a particle into its anti-particle, and vice-versa : X → X.

Parity symmetry is conserved in strong and in electromagnetic interactions. The conservation of parity was assumed to be a universal law. However, in the mid 1950s Chen Ning Yang and Tsung-Dao Lee suggested that the weak interaction, might violate this law [START_REF] Lee | Question of Parity Conservation in Weak Interactions[END_REF]. Indeed, parity violation of the weak interaction was confirmed in the famous 60 Co experiment by Chien Shiung Wu and collaborators [START_REF] Wu | Experimental Test of Parity Conservation in β Decay[END_REF], earning Yang and Lee the 1957 Nobel Prize in Physics. This and further experiments showed that only left handed neutrinos and right handed anti-neutrinos exist. In other words only one single helicity, i.e the projection of spin on the momentum direction, state exist for neutrinos. Hence, both C and P symmetries are violated.

Standard Model

Another experiment was performed later by Lederman [START_REF] Garwin | Observations of the Failure of Conservation of Parity and Charge Conjugation in Meson Decays: The Magnetic Moment of the Free Muon[END_REF], which allowed the observation of parity violation in charged pion decay. In this experiment the combined CP symmetry was proposed as an symmetry of nature representing the true symmetry between matter and antimatter where taking the mirror image of a physical system and replacing every particle with its antiparticle would result in exactly the same phenomena as before. The weak interaction seemed to violate P and C in a way that combined CP is conserved. However, in the mid 1960s, James Cronin, Val Fitch and coworkers provided an experimental demonstration that also CP symmetry is violated in certain weak processes [START_REF] Christenson | Evidence for the 2π Decay of the K 0 2 Meson[END_REF], in particular, in decays of neutral kaons. Beside the discovery that CP symmetry violation, the quantitative value of the observed violation was intriguing. It took nearly ten years for the breakthrough in understanding how the observed CP violation can be connected with the emerging structure of the Standard Model (SM) of particle physics. In 1973 Makoto Kobayashi and Toshihide Maskawa pointed out that in the case of three quark generations the number of degrees of freedom in the SM naturally gives rise to the CP violating complex phase in the 3 × 3 quark mixing matrix, now known as the Cabibbo-Kobayashi-Maskawa (CKM) matrix [START_REF] Kobayashi | CP Violation in the Renormalizable Theory of Weak Interaction[END_REF] (note that in 1973 only the u, d, s quarks were known. 1 Indeed, two new quarks were discovered soon after, c (1974) and b (1977), and finally also t in 1995).

The CKM matrix is an elegant way to encode information on the relative strength of flavor changing weak decays, predicting correlations between different quark decays and CP violating observables.

In the following section we elaborate the origin of CP violation which is manifested in the electroweak interaction, starting by the mathematical description of the SM that is summarized by its Lagrangian:

L SM = L kinetic + L Higgs + L Yuk
The kinetic term describes the dynamics of the spinor fields ψ L kinetic = iψ(δ µ γ µ )ψ, where ψ ≡ ψ † γ 0 and the spinor fields ψ are the three fermion generations, each consisting of the following five presentations:

Q I Li (3, 2) +1/6 , u I Ri (3, 1) -2/3 , d I Ri (3, 1) +1/3 , L I Li (1, 2) -1/2 , ℓ I Ri (1, 1) +1 ,
This notation means that

Q I i (3, 2) +1/6 is SU(3) C triplet, left-handed SU(2)
L dou- blet, with hypercharge Y = 1/6. The superscript I implies that the fermion

Standard Model

fields are expressed in the interaction basis. The subscript i stands for the three generations.The subscript L indicates that only left handed fermions transform non-trivially under isospin, they belong to an isodoublet, while right handed fermions belong to an isosinglet.

The interaction terms are obtained by imposing gauge invariance by replacing the partial derivative with the covariant derivate

L kinetic = iψ(D µ γ µ )ψ,
with the covariant derivative defined as Next, the W and Z bosons aquire their mass through the mechanism of spontaneous symmetry breaking. For this, the Higgs scalar field and its potential is added to the Lagrangian: 2 where φ(x) is an isospin doublet:

D µ = δ µ + ig s G µ a L a + igW µ b σ b + ig ′ B µ Y,
L Higgs = (D u φ) † (D µ φ) -µ 2 φ † φ -λ(φ † φ)
φ(x) = φ + φ 0
The coupling of the Higgs to the gauge fields follows from the covariant derivative in the kinetic term. However, the interactions between the Higgs and the fermions, the Yukawa couplings, have to be added by hand and this is where CP violation can only arise from,

-L Yukawa = Y d ij Q I Li φd I Rj + Y u ij Q I Li φu I Rj + Y ℓ ij L I Li φℓ I Rj , (1.1)
where the Higgs representation is φ and ( φ = iσ 2 φ * )and Y u,d,l are 3× 3 arbitrary complex matrices that operate in flavor space giving rise to couplings between different families, or quark mixing, and thus to the field of flavour physics.

The interesting part lies in the quark mass terms, which we further spell out:

φ(x) = φ + φ 0 sym.breaking -------→ 1 √ 2 0 ν + h(x)
,

Standard Model

the following mass terms for the fermion fields arise:

-L quarks Yukawa = Y d ij Q I Li φd I Rj + Y u ij Q I Li φu I Rj + h.c = Y d ij d I Li ν √ 2 d I Rj + Y u ij u I Li ν √ 2 u I Rj + h.c + interaction terms = M d ij d I Li d I Rj + M u ij u I Li u I Rj + h.c + interaction terms (1.2)
where the interaction terms of the fermion fields to the Higgs field, qqh(x) are omitted and

M d ij = (ν/ √ 2)Y d ij , M u ij = (ν/ √ 2)Y u ij , (1.3)
are the 3 × 3 complex matrices that couple the left-handed component of each quark Q I Li with the rights-handed projections of all flavours. Thus, they are non-diagonal in the flavour basis. The mass eigenstates being the ones that propagate in space and time, the matrix M must be diagonalized:

M d diag = V d L M d V d † R M u diag = V u L M u V u † R
Using the requirement that the matrices V are unitary (V d † L V d L = 1) the Lagrangian can now be expressed as follows: .4) where the matrices V are absorbed in the quark states, resulting in the following quark mass eigenstates:

-L quarks Yukawa = d Li (M d ij ) diag d Rj + u Li (M u ij ) diag u Rj + hc. + .... ( 1
d Li = (V d L ) ij d I Lj , u Li = (V u L ) ij u I Lj d Ri = (V d R ) ij d I Rj , u Ri = (V u R ) ij u I Rj (1.5)
When expressing the SM Lagrangian in terms of the primed mass-eigenstate fields, the quark kinetic terms remain unchanged. The Z and γ boson couplings are also unaffected. As a consequence no flavour-changing neutral current (FCNC) processes are allowed at the tree level in the SM. On the other hand, in the part of the charged-current Lagrangian describing the couplings of the W ± bosons to the left handed quarks, the transformation leaves the couplings unchanged by V u L , but not by

V u † R V d L : L kinetic,cc (Q L ) = g √ 2 u I iL γ µ W -µ d I iL + h.c..= g √ 2 u iL γ µ (V u L V d † L ) ij d Lj W -µ + h.c.. (1.
6) The unitary 3 × 3 matrix

V CKM = (V u L V d † L ) ij Standard Model
is the Cabibbo-Kobayashi-Maskawa (CKM) mixing matrix [17] [16]. CP violation shows up in the complex Yukawa couplings. We examine once more the Yukawa part of the Lagrangian, L Yukawa , focussing on the charged current couplings in the basis of quark mass eigenstates:

L kinetic,cc (Q L ) = g √ 2 u iL γ µ V ij W -µ d iL + g √ 2 d iL γ µ V * ij W +µ u iL (1.7)
and the CP-transformed expression :

L kinetic,cc (Q L ) = g √ 2 d iL γ µ V ij W +µ u iL g √ 2 u iL γ µ V * ij W -µ d iL . (1.8)
Then we can conclude that the Lagrangian is unchanged if

V * ij = V ij .
The complex nature and the dimension of the CKM matrix, V CKM , is the origin of CP violation in the Standard Model. In the following section, the properties of the CKM mixing matrix will be examined in detail.

The Cabibbo-Kobayashi-Maskawa Matrix

Unitarity traingle

In the general case of n quark families, the 2n 2 real parameters of the complex n × n matrix V CKM , can be reduced using properties of the V CKM matrix and the quarks fields as follows.

1. The Unitarity condition (V † V = 1) reduces the number of parameters to n 2 .

2. The phases of the quarks can be rotated freely, since the overall phase is irrelevant , 2n-1 relative quark phases can be removed.

These leaves V CKM matrix with 2n 2n 2 -(2n -1) = (n -1) 2 free parameters. These parameters can be divided into n(n -1)/2 Euler angles describing the rotations among the n dimensions, leaving 1 2 (n -1)(n -2) irreducible phases that turn out to be 0 for n = 1 and 2 for n = 3. As Kobayashi and Maskawa noticed, this irreducible phase in a three-generation model would be the origin of all CP violation in the SM. The bottom and the top quark were discovered in 1977 and 1994 respectively. In 2008 Kobayashi and Maskawa were awarded the Nobel prize for the discovery of the origin of the broken symmetry which predicts the existence of at least three families of quarks in nature.

Looking again at the consequences of the unitarity condition for the V CKM matrix:

V † V = VV † = 1,

Standard Model

leads to the first following relations:

V ud V * ud + V us V * us + V ub V * ub = 1, V cd V * cd + V cs V * cs + V cb V * cb = 1, V td V * td + V ts V * ts + V tb V * tb = 1.
(1.9)

These relations express the so-called weak universality, because it shows that the squared sum of the coupling strengths of the u-quark to the d, s and b-quarks is equal to the overall charged coupling of the c-quark (and the t-quark ). In addition, we see that this sum adds up to 1, meaning that "there is no probability remaining" to couple to a 4 th down-type quark. Another three additional interesting equations arise from the unitary relation:

V * ud V us + V * cd V cs + V * td V ts = 0, (1.10) V * us V ub + V * cs V cb + V * ts V tb = 0, (1.11) V * ud V ub + V * cd V cb + V * td V tb = 0. (1.12)
Each term in these relations can be interpreted geometrically as a vector in the complex plane. This way, each equation above can be visualized as a triangle in the Argand plane, known as the unitarity triangles.

Since the first formulation of the V CKM matrix, several parametrization have been proposed. One of such parametrization is the so called "Standard parametrization" proposed by Chau and Keung, and which is obtained as the product of three (complex) rotation matrices and a overall phase, where c ij = cosθ ij , s ij = sinθ ij for i < j = 1, 2, 3, the θ ij are the three rotation angles between families, and δ is the irreducible phase. The phase is chosen here to appear in the matrix describing the relation between the 1 st and 3 rd family. Thanks to many experimental results, it has been established that a hierarchy among the matrix elements exists and that the matrix is dominated by its diagonal terms. In other words, transitions among quarks from different flavour doublets are suppressed, compared to the ones among quarks of the same generation. A useful parameterization that emphasizes the hierarchical, nearly diagonal structure of the matrix, is due to Wolfenstein.

V CKM =   c 12 c 13 s 12 c 13 s 13 e -iδ
V CKM =   V ud V us V ub V cd V cs V cb V td V ts V tb   ≃    1 -λ 2 2 λ λ 3 A(ρ -iη) -λ 1 -λ 2 2 λ 2 A λ 3 A(1 -ρ -iη) -λ 2 A 1   
which is based on a Taylor development where λ is the expansion parameter, known to be small from experimental data, i.e λ ≃ |V us | ∼ 0.22 and A, ρ and η are all of order 1. In the Wolfenstein parametrization η contains the CP violation information. i.e CP violation occurs when η doesn't equal 0 and the triangles do not collapse to a line. To all orders in λ, the exact Wolfenstein parameterization can be defined as,

s 12 ≡ λ (1.14)
s 23 ≡ λ 2 A (1.15) s 13 e -iδ ≡ λ 3 A(ρ -iη) (1.16)
This definition is useful because it allows an elegant improvement of the accuracy of the original Wolfenstein parameterization. In particular, up to the order O(λ 6 ), one get

V us = λ, V cb = λ 2 A, V ub = λ 3 A(ρ -iη), V td = λ 3 A(1 -ρ -i η) Img(V cd ) = -λ 5 A 2 η, Img(V ts ) = -λ 4 Aη, where ρ = ρ(1 - ρ 2 2 ), η = η(1 - λ 2 2 )
One of the major physics goal of the B Factories was to improve the experimental constraints on the elements of V CKM . Let us now return to the three relations 1.11-1.12 that give rise to the unitarity triangles. The first two triangles are related to the CKM matrix elements that governs the K 0 -K 0 and B 0 s -B 0 s systems, respectively. For each of those triangles one side is much shorter than the other two, and so they almost collapse to a line. This would give an intuitive understanding of why CP violation is small in the leading K and B s decays. On the other hand, for the triangle corresponding to the relation given in Equation 1.12, the sides are of the same order of magnitude. It is in this third triangle,related to the B 0 d -B 0 d system, that the most exciting physics of CP violation lies. Indeed,

Standard Model

the openness of this triangle predicts large CP asymmetries in B d decays. Note that all the unitarity triangles are equal in area. Equation 1.12 can be written in another way. Once divided by V cd V * cb it becomes

V ud V * ub V cd V * cb + 1 + V td Vtb * V cd V * cb = 0.
In this convention one of the side of this triangle is aligned to the real axis of the Argand plane. The resulting pictorial representation is a unitarity triangle whose apex is determined by the ρ and η parameters, or equivalently, the irreducible phase (see Figure 1.2). In this representation, the lengths of the sides are given by CB = 1, (1.17)

AB = V td V * tb V cd V * cb = (1 -ρ) 2 + η2 = 1 λ V td V cb , (1.18) AC = V ud V * ub V cd V * cb = ρ2 + η2 = (1 - λ 2 2 ) V ub V cb , (1.19)
while the angles are given by (quoting both notation with (α, β, γ) and (φ 1 , φ 2 , φ3))

φ 2 = α = arg V td V * tb V cd V * cb (1.20) φ 1 = β = arg V td V * tb V cd V * cb = arctan η 1-ρ
(1.21)

φ 3 = γ = arg V ud V * ub V cd V * cb = arctan η ρ (1.22) π = α + β + γ (1.23)
These parameters have been measured in various B decay modes by independent experiments. The SM description of CP violation can be tested by analysing these measurements and checking if the apex of the triangle coincides, as expected in the SM, among the various measurements. The current experimental status of these parameters are summarized in Figure 1.3. In the next chapter, we shall focus on these measurements, especially the angle β. We will also explore the sensitivity to New Physics of one observation of CP violation. CHAPTER 2

Standard Model

Mixing and CP violation in neutral B meson

This chapter presents the quantum mechanical properties of the neutral B 0 meson system, which are model independent. These properties are related to CP violation observables, and use features of the flavor and weak-interaction structure of the Standard Model. Three kinds of CP violation resulting from different processes, are distinguished allowing to extract different CP-violating quantities. The connection of these quantities with new physics in b → s γ transitions is discussed, finalizing with a summary of the previous experimental results for the CP-violating parameters for the two radiative B 0 decays channels analysis presented in this thesis.

Mixing of neutral B meson

A neutral meson state and its CP conjugate decay due to weak interactions. In order to describe the neutral meson system it is important to distinguish between different representations. On one hand, the neutral meson can be described by two flavor eigenstates, each with a definite quark content, which are useful for understanding particle production and decay processes. On the other hand, the neutral meson can be described by the two eigenstates of the Hamiltonian(mass eigenstates), with definite mass and lifetime, which are the states that propagate in space and time. Mass eigenstates are not flavor eigenstates, and so flavor eigenstates get mixed as they propagate. Since CP is broken in the SM, the mass and CP eigenstates can differ. The phenomenon of mixing, referring here to the process where a neutral meson turns into its antiparticle via a process involving two charged currents, has been observed in kaons [START_REF] Lande | Observation of Long-Lived Neutral V Particles[END_REF], B d and B s mesons [START_REF] Albrecht | ARGUS, Observation of B0 -anti-B0 Mixing[END_REF], and also, D mesons [START_REF] Aubert | BaBar, Evidence for D 0 -D 0 Mixing[END_REF].

Let us now consider an arbitrary combination of the neutral B-meson flavor eigenstates1

|ψ(t) = a(t)|B 0 + b(t)|B 0 (2.1)
Its time evolution is given by the Schrödinger equation with the effective Hamiltonian

H ih ∂ ∂t |ψ(t) = H|ψ(t) , (2.2)
Where in the |B 0 , |B 0 basis,

|ψ(t) = a(t) b(t) (2.
3)

H = M - i 2 Γ = |ψ(t) = M 11 -i 2 Γ 11 M 12 -i 2 Γ 12 M 21 -i 2 Γ 21 M 22 -i 2 Γ 22 (2.4)
H is composed of the mass matrix M and the decay matrix Γ, both of which are 2 × 2 hermitian matrices. Assuming the CPT theorem valid , the following relations hold :

M 21 = M * 12 , Γ 21 = Γ * 12 , M 11 = M 22 = M , Γ 11 = Γ 22 = Γ (2.5)
that means that the mass and the total decay width of particles and antiparticles are identical. The off-diagonal terms, M 12 and Γ 12 are particularly important in the discussion of CP violation, since arg(M 12 /Γ 12 ) = 0 would be implied in the case of CP conservation. The mass matrix of the Hamiltonian describes the oscillation between flavor eigenstates, where the diagonal terms in M are dominated by the flavor eigenstates masses, and the off-diagonal ones represent the transitions via virtual intermediate states. The diagonal terms of the decay part of the Hamiltonian describe the flavor eigenstates decays to different final states, i.e B 0 → f and B 0 → f , while the off-diagonal terms describe the transition via real intermediate states. Figure 2.1 shows the Feynman diagrams representing the weak transitions between B 0 and B 0 via second order transitions (transitions with two quarks), also referred to as B 0 B 0 mixing. Such transitions lead to the inclusion of the three up-type quarks in the loop, since all of them couple via a CKM factor that is proportional to λ 6 . However, integration of the internal degrees of freedom (the up-type quarks and the W) yields an expression that weighs the contribution of each quark by the ratio of its mass to that of the weak boson. Thus, the up and charm quarks contribution are suppressed, and an evaluation of the corresponding CKM factors readily gives a phase of

(V td V * tb ) 2 ∼ e -i2β
. In other words, the B 0 states that oscillate into B 0 pick up an extra -2β phase, called the mixing angle, with respect to the B 0 states that do not oscillate. This phase is measurable whenever both flavors decay to a common state.

Diagonalizing the Hamiltonian, H, leads to the expression of the mass eigenstates of the neutral B meson system, which consist in a superposition of the B 0 and B 0 flavor eigenstates, such as

|B L = p|B 0 + q|B 0 (2.6
)

|B H = p|B 0 -q|B 0 (2.7)
where the index L(H) refers to the lighter (heavier) mass eigenstates of the neutral and the complex coefficients p and q are constrained by a normalization condition

|p 2 | + |q 2 | = 1. (2.8)
We can find p and q by solving

M -i 2 Γ M 12 -i 2 Γ 12 M * 12 -i 2 Γ * 12 M -i 2 Γ p q = λ H,L p q (2.9)
where λ ± are the eigenvalues of the mass-decay matrix,

λ L = m L - i 2 Γ L , λ H = m H - i 2 Γ H (2.10)
where m L and m H are the masses of the eigenstates |B L and |B H , respectively. It is useful then to define the average mass and width as well as the mass and width differences between the neutral B 0 mesons as :

M = m H + m L 2 = M 11 = M 22 , ∆m d ≡ M H -m L (2.11) Γ = Γ L + Γ H 2 = Γ 11 = Γ 22 , ∆Γ ≡ Γ H -Γ L (2.12)
where ∆m d is positive and represents the mixing frequency of the B 0 B 0 oscillation. Finally one can derive the ratio of q p from Equation 2.9. Consider a state which is created at time t = 0 as an initially pure B 0 (B 0 ), denoted as |B 0 (t) |B 0 (t) , The time evolution of these states can be described by the eigenvalues of the Hamiltonian and the q and p parameters such as:

q p = ± M * 12 -i 2 Γ * 12 M 12 -i 2 Γ 12 . ( 2
|B 0 (t) = g + (t)|B 0 + q p g -(t)|B 0 , (2.17) |B 0 (t) = g + (t)|B 0 + q p g -(t)|B 0 , (2.18)
where

g ± (t) = e -iMt-1 2 Γt [1 ± e -i∆m d t+ 1 2 ∆Γt ] (2.19)
Here Γ fulfills the natural role of decay constant, Γ = 1/τ. The sign of ∆m d is by definition positive, but the sign of ∆Γ has to be determined experimentally. Due to the close values of the B 0 meson lifetime, τ = (1.52 ± 0.004) ps [START_REF] Tanabashi | Review of Particle Physics[END_REF] and the frequency of oscillation, ∆m d = (0.507 ± 0.005) ps -1 , the amplitude for the mix- ing process is rather large. Accordingly, the integrated probability of oscillation is sizable [START_REF] Amhis | Averages of b-hadron, c-hadron, and τ-lepton properties as of summer 2016[END_REF].

χ = (τ∆m d ) 2 2(1 + (τ∆M) 2 = 0.1878 ± 0.0024 (2.20)
which confers mixing a prominent role. An immediate consequence are the large time dependent CP asymmetries that mixing produces, and that are discussed in the next section.

Decay rates

In this section we extend the formalism of neutral meson oscillations, and include the subsequent decay of the meson to a final state f. We consider the following decay amplitudes:

A f = f |H|B A f = f |H|B (2.21)
and define the complex parameter λ f

λ f ≡ 1 λ f ≡ q p A f A f (2.22)
The general expression for the time dependent decay rates is,

Γ B→ f (t) = | f |H|B(t) | 2 (2.23)
which gives us the probability that the state |B at t = 0 decays to the final state f at time t. Now and using the Equations 2.17 and 2.18 we find:

Γ B→ f (t) = |A f | 2 (|g + (t)| 2 + |λ f | 2 |g -(t)| 2 + 2Re[λ f g * + (t)g -(t)]) (2.24)
Γ B→ f (t) = |A f | 2 p q 2 (|g -(t)| 2 + |λ f | 2 |g + (t)| 2 + 2Re[λ f g + (t)g * -(t)]) (2.25)
The terms proportional |A| 2 are associated with decays that occurred without oscillation, whereas the terms proportional to |A| 2 (p/q) 2 are associated with decays following a net oscillation. The third terms, proportional to Re(g * g) are associated to the interference between the two cases. Following this, the next session we will state the classification between the various types of CP violation that may occur.

CP violation in the B meson system

To measure CP violation, we measure the asymmetry between the decays of B 0 (t) and B 0 (t) into the CP conjugated final states, f and f . This asymmetry depends on time, since decay rates also depend on time,

a f (t) = Γ(B 0 (t) → f ) -Γ(B 0 (t) → f ) Γ(B 0 (t) → f ) + Γ(B 0 (t) → f ) (2.26)

CP violation in decay

CP violation in decay or called "Direct CP violation", which occurs when the amplitude for a decay and its CP conjugate have different magnitudes It is independent of B 0 B 0 mixing effects and can also be observed in the decays of Mixing and CP violation in the B meson system charged B mesons.

CP violation in mixing

Another type of CP violation comes from the fact that the neutral B mesons can oscillate into its CP conjugate as described in Sec 2.1. Indeed, since the mass and the CP eigen-states are not identical in the case of neutral B mesons, an asymmetry arises between their transition probabilities, B → B 0 and B 0 → B 0 One can express these differences using the convention-free quantity |q/p|, since it is related to the matrix elements M [START_REF] Christenson | Evidence for the 2π Decay of the K 0 2 Meson[END_REF] in the neutral kaon system. In the B 0 d system, effects of CP violation in mixing is expected to be small, O (10 -4 ) and very negligible with respect to the sensitivity of the B factories, thus making |q/p| ∼ 1 a good approximation.

CP violation in the interference between decays with and without mixing

Finally, another possibility for CP violation, also referred to as CP violation in mixing and decay, it occurs whenever

Γ(B 0 → f ) = Γ(B 0 → f ) (2.28)
where f is a final state accessible to both B 0 and B 0 , a condition that is satisfied if the final state f is a CP eigenstate. In this case CP violation arises as a consequence of the interference between the amplitudes (AB 0 → f CP ) and A(B 0 → B 0 → f CP ). Note that CP violation in the mixing and in the decay of K 0 -K 0 system [15], had also been observed before the start of the B Factories.

A quantity similar to the one used to measure purely direct CP violation, given in Equation 2.26, could be applied in order to measure the CP violation here. However, in this case the flavor of neutral B mesons is not straight forward to determine since, precisely, their flavors change over time. At the B Factories, the flavor determination is facilitated by the fact that the B mesons are produced from the decay of the Υ(4S) resonance, i.e. Υ(4S) → B 0 B 0 , therefore forming an entangled pair of mesons. Such states are predicted by quantum mechanics by the famous "EPR paradox" [START_REF] Einstein | Can quantum mechanical description of physical reality be considered complete?[END_REF], where at instant t, the probability of one of the mesons to be a particle equals the probability for the other meson to be an antiparticle. Thus, if it is possible to determine the flavor of one of the B mesons at time t, the flavor of the other meson can be inferred to be the opposite at that exact same instant, and evolves afterwards independently by means of mixing. This is experimentally known as flavor tagging, which will be discussed more in Mixing and CP violation in the B meson system section 4.1.1. The flavor of a given B meson, B rec , is determined from the observation of the other meson, called B tag , decaying into a state that unambiguously determines its flavor. A precise measurement of the time elapsed between the two decays, ∆t is also required in order to account for the probability for a given B meson state to oscillate. With these considerations, the CP asymmetry can be defined in a time dependent way:

a CP (∆t) = Γ(B tag=B 0 (∆t) → f CP ) -Γ(B tag=B 0 (∆t)→ f CP ) Γ(B tag=B 0 (∆t) → f CP ) + Γ(B tag=B 0 (∆t)→ f CP ) (2.29)
In the case where no experimental biases are taken into account, such as the probability of the wrongly determining the flavor of the B tag meson called mistagging, (which will be developed more later in the section ), the amplitudes for the processes B 0 (∆t) → f CP and B 0 (∆t) → f CP are given by:

A f CP = f CP |H|B 0 (2.30) A f CP = f CP |H|B 0 (2.31)
First we can simplify the decay rates in Equation 2.24 and 2.25 by taking into account ∆Γ ≪ Γ and the definition of λ f and λ f in Equation 2.22 where

Γ(B 0 (t) → f CP ) ∝ e -Γt |A f CP | 2 1 + 1 -|λ f CP | 2 1 + |λ f CP | 2 cos(∆Mt) - 2Imλ f CP 1 + |λ f CP | 2 sin(∆Mt) (2.32) Γ(B 0 (t) → f CP ) ∝ e -Γt |A f CP | 2 1 - 1 -|λ f CP | 2 1 + |λ f CP | 2 cos(∆Mt) + 2Imλ f CP 1 + |λ f CP | 2 sin(
S = 2Imλ f CP 1 + |λ f CP | 2 , A = |λ f CP | -1 |λ f CP | + 1 (2.35)
Remembering that A f = 1 and q p = 1 respectively. However in this present case, even if

λ f CP = q p A f CP A f CP (2.
A f A f = q p = 1, CP violation could still occur through |λ f cp | = 1, Img(λ f cp = 0) (2.38)
If there is only one SM contribution to the amplitudes A f and A f , the expectations are that S = -η CP sin(2β), where the factor η CP accounts for the CP eigenvalue of the final state. and A = 0. Deviations from that imply the existence of unaccounted amplitudes that, depending on the characteristics of the mode, could originate from theoretical uncertainties in the Standard Model contributions, or could be an indication of physics beyond the SM.

CP violation in b → s γ transitions 2.3.1 Trees and Penguins

In a quantum field theory, on which is based the SM, in order to describe a given decay process, one needs to include all the possible contributing amplitudes. Each amplitude does not necessarily contribute at the same level, thus it is useful to apply a hierarchical ranking. It often happens that only the two first-order contributions to the total amplitude are sufficient to make theoretical predictions that are precise enough to be compared to experimental results. For instance, in the so-called "golden mode" B 0 → J/ψK 0 S in which the final state is a CP eigenstate that makes it sensitive to CP violation in mixing and decay, not only one amplitude is allowed. One of the contributing amplitudes, in which the W boson is emitted and absorbed by the same quark line, is called a "loop" or, more often, a "penguin" diagram, whereas the other, is said to be a "tree-level", or simply "tree", diagram, both amplitudes sown in Figure 2.2. In the penguin diagram, the internal loop, which is formed by the W boson and a combination of up-type quarks, is dominated by the top quark due to its large mass compared to up and charmed quarks. In the hypothetical presence of new physics, new heavy particles could traverse the loop and provide new CP-odd phases that could dramatically enhance (or suppress) the amplitude [START_REF] Grossman | CP asymmetries in B decays with new physics in decay amplitudes[END_REF]. As shown in and gluinos from a super symmetric model(SUSY) [START_REF] Martin | A Supersymmetry primer[END_REF], an example of NP models that bring extra source of flavor violation.

In the considered example, the CKM factors in both amplitudes carry the same phases, as can easily be seen thanks to the powers of λ and phases that have been written next to the CKM terms on the figure. However, as in many other decays, the penguin diagram is suppressed compared to the tree diagram [START_REF] Nir | CP violation in meson decays[END_REF], which have SM couplings. Thus, SM contributions in the loop dominates over possible effects from non-SM couplings and a clean interpretation for the timedependent asymmetry is obtained: a CP (∆t) = sin(2β) sin(∆m d ∆t). The measurement of CP violation in this channel constitutes one of the main achievements of the B Factories. In a general way, tree diagrams are usually cleaner in their theoretical interpretation than penguin diagrams. However, in some specific transition modes, the tree diagrams can be suppressed compared to penguin diagrams, as it is the case for b → s transitions. Furthermore, since SM parameters are now well constrained, any deviations due to unknown physics should be small compared to SM predictions. Such modes are therefore particularly interesting in the indirect search for new physics at the electroweak scale, due to the absence of a tree contribution which could overshadow effects from possible new physics. They are also complementary to direct searches performed in high-energy colliders such as in hadronic colliders like the LHC.

Photon polarization in radiative B 0 decays

Study of FCNC processes(flavor-changing neutral current), such as b → sγ transitions, can provide strong constraints on NP(New Physics). In the SM, the Glashow-Iliopoulos-Maini (GIM) mechanism implies that FCNC processes are forbidden at the tree level and only occurs through a loop or box diagrams, where heavy virtual particles can propagate. Since the presence of such heavy particles influences the predicted values of physical observables, the study of b → sγ processes could reveal the existence of yet unknown particles introduced by NP models. The SM predicts that photons emitted in b → sγ decays are lefthanded, up to small corrections of order m s /m b , while being right-handed in b → sγ. In several models beyond the SM the photon in b → sγ acquires an appreciable right-handed component due to the exchange of a heavy fermion in the electroweak loop process. In this context, many NP models models [START_REF] Cho | b -> s gamma decay in SU(2)-L x SU(2)-r x U(1) extensions of the Standard Model[END_REF] [29] predicts right-handed component may be comparable in magnitude to the lefthanded component, without affecting the SM prediction for the inclusive radiative decay rate, which motivates independent measurements of the photon helicity in several exclusive radiative decay modes.

In the SM, the quark level b → sγ vertex is given (without QCD corrections) by:

sΓ b→sγ µ b = e (4π) 2 g 2 2M 2 W V * ts V tb F 2 siσ µν q ν (m b P R + m s P L )b, (2.39)
where q = q bq s with q being the four-momenta of the b and s quarks, respectively, F 2 is the loop function, whose expression can be found in [START_REF] Inami | Effects of Superheavy Quarks and Leptons in Low-Energy Weak Processes k(L) -> mu anti-mu, K+ -> pi+ Neutrino anti-neutrino and K0 <-> anti-K0[END_REF], V ts and V tb are the leading CKM matrix elements appearing in the loop diagram, and σ µν are the commutators of the Dirac γ 4 × 4 matrices. P L and P R are the projection operators defined as

P L = 1 2 (1 -γ 5 ), P R = 1 2 (1 + γ 5 ). (2.40)
In Equation 2.39, the term proportional to m b describes b → sγ L transitions, while the term proportional to m s describes b → sγ R transitions. Therefore, due to the fact that the b quark is much heavier than the s quark (i.e. m s /m b ∼ 0.02), the SM predicts that photons emitted in b → sγ decays are predominantly lefthanded. In a similar manner, photons emitted in b → sγ decays are predominantly right-handed.

Physical observables and experimental status

As the photon polarization is not directly measurable, there are different methods proposed to measure it in b → sγ processes. One of this methods, which is adopted in this thesis, is covered in this section.

Mixing and CP violation in the B meson system

Mixing-induced CP asymmetry

One way to probe the photon helicity is to perform an indirect measurement via a time-dependent CP asymmetry analysis in neutral B mesons. In the case of the radiative decay of a neutral B meson to a hadronic CP eigenstate f CP , B 0 (t) → f CP γ, where the B meson state is identified (tagged) as a B 0 (rather than a B 0 ) a time t = 0, the time-dependent CP asymmetry is given by [3]

a CP (t) = Γ(B 0 (t) → f CP γ) -Γ(B 0 (t) → f CP γ) Γ(B 0 (t) → f CP γ) + (B 0 (t) → f CP γ (2.41) ≃ -ξ sin(2ψ) sin(φ M -φ L -φ R )sin(∆Mt) (2.42) = S f CP sin(∆Mt) (2.43)
where S f CP is the mixing induced CP violation parameter, ξ ≡ CP( f CP ) = ± 1 and

Γ(B 0 (t) → f CP γ) = |M L (t)| 2 + |M R (t)| 2 ,
(2.44)

Γ(B 0 (t) → f CP γ) = |M L (t)| 2 + |M R (t)| 2 , ( 2.45)
with M L and M R corresponding to the total amplitude involving left-handed and right-handed photons, respectively. In order to obtain to obtain the second equation 2.42, both direct CP violation (a f CP ) and the small width difference, compared to the mass difference between the B meson mass eigenstates, are neglected.

In Equation 2.42, sin(2ψ) parametrizes the relative amount of left-handed and right-handed photons and is defined as

sin(2ψ) ≡ 2|M L M R | |M L | 2 + |M R | 2 ;
(2.46) note that the phase φ M is the one appearing in the B 0 B 0 mixing such as φ M = 2β for B d mesons and is almost zero for B s mesons; φ L,R are the relative CP-odd weak phases in the b → sγ process,

φ L,R = sin -1 ( Img(M L,R ) |M L,R | ) (2.47)
In the SM, φ L,R are predicted to be almost zero O(λ 4 ). Since the right-handed amplitude in suppressed in the SM, the time-dependent asymmetry is such as

a SM CP (t) ∼ 0 (2.48)
From this method, it appears that, although an observation of a CP (t) = 0 would immediately indicate the existence of NP contributions, it is not possible to determine quantitatively the ratio M R /M L . Indeed a CP (t) measures a combination

Mixing and CP violation in the B meson system of M R /M L and the CP violating phases in b → sγ as well as in BB mixing. Therefore in the case of an experimental result that would measure a deviation of a CP (t) from its predicted value in the SM, one can only fix the CP violating phases φ M,L,R as given by several NP models in order to best describe the observed value of a CP (t).

Several exclusive radiative decay modes have been studied in time-dependent CP violation analyses. Two of such are, B 0 → K 0 S π 0 γ and B 0 → K 0 S π + π -γ. These analysis are very challenging in hadronic colliders, and the best results to date come from the B Factories.

Summary of previous experimental results for

B 0 → K 0 S π 0 γ and B 0 → K 0 S π + π -γ
In B 0 → K 0 S π 0 γ decay process, where the SM predicts S ≃ -0.028 [START_REF] Atwood | Mixing induced CP asymmetries in radiative B decays in and beyond the standard model[END_REF], both BABAR and Belle have have performed measurements of the mixing-induced CP asymmetry parameter S, and reported S B 0 →K 0 S π 0 γ = -0.78 ± 0.59 ± 0.09 [START_REF] Aubert | Measurement of Time-Dependent CP Asymmetry in B 0 → K 0 S π 0 γ Decays[END_REF] and S B 0 →K 0 S π 0 γ = -0.10 ± 0.31 ± 0.07 [START_REF] Ushiroda | Belle, Time-Dependent CP Asymmetries in B 0 → K 0 S π 0 γ transitions[END_REF],respectively. where B 0 → K 0 S π 0 γ goes through K * 0 (892). Also measurement of the direct CP asymmetry in BABAR and Belle was performed, A B 0 →K 0 S π 0 γ = -0.36 ± 0.33 ± 0.05 and A B 0 →K 0 S π 0 γ = -0.2 ± 0.2 ± 0.06 respectively.

In B 0 → K 0 S π + π -γ decay process, where the SM predicts S ≃ [], both BABAR and Belle have have performed measurements of the mixing-induced CP asymmetry parameter S, and reported S B 0 →K 0 S π + π -γ = 0.14 ± 0.25 ± 0.03 [START_REF] Del Amo | BaBar, Time-dependent analysis of B 0 → K 0 S ππ + γ decays and studies of the K + ππ + system in B + → K + ππ + γ decays[END_REF] and S B 0 →K 0 S π + π -γ = -0.09 ± 0.27 +0.04 -0.07 [START_REF] Li | Belle, Time-dependent CP Asymmetries in B 0 → K 0 S rho 0 γ Decays[END_REF],respectively. where B 0 → K 0 S π + π -γ goes through K * 0 (892). Also measurement of the direct CP asymmetry in BABAR and Belle was performed, A B 0 →K 0 S π + π -γ = -0.39 ± 0.2 +0.03 -0.02 and A B 0 →K 0 S π + π -γ = -0.2 ± 0.2 ± 0.06 respectively. From the list of previous measurements and results, one can see that the measurements where statistically limited for the mixing-induced CP asymmetry parameter S and for the direct CP asymmetry A results in good agreement with the SM prediction and the assumption made in Equation 2.42.

CHAPTER 3

SuperKEKB and Belle II project

There is two ways to look for physics beyond the standard model: one way is to reach high energies in order to produce directly new heavy particles, which is known as energy frontier. Other option is to look for new physics by performing precision measurements at lower energy with the highest liuminosity, known as intensity frontier. The Large Hadron Collider at CERN, is an example of the energy frontier while electron-positron colliders at B factories belong to the intensity frontier type. B factories have been crucial in the the past decades to establish the CKM mechanism and to provide precision tests of the SM as well as a complementary tool to the energy frontier experiments for the search of forbidden processes and new physics. The Belle II detector operating at the Su-perKEKB, an electron-positron collider, at KEK laboratory in Tsukuba (Japan), aims to explore new physics with an unprecedented luminosity. SuperKEKB will provide Belle II a data set which is 50 times that data provided by its predecessor KEKB [START_REF] Kurokawa | Overview of the KEKB accelerators[END_REF]. In the following section 3.1 an overview of the SuperKEKB accelerator and its upgrades with respect to its predecessor KEKB is given, then a description of the different Beam-Induced Backgrounds due to the high luminosity and design upgrades are listed. The last part of the chapter 3.2 will be devoted to the description of three running phases of SuperKEKB, concluding with the luminosity prospects and future plans for the accelerator, which plays a crucial role in determining the physics reach of Belle II.

SuperKEKB

SuperKEKB is an asymmetric e + e -collider, that operate at a center-of-mass energy √ s = 10.58 GeV, corresponding to the invariant mass of the Y(4S) resonance, which is a bound state (bottomonium) of the beauty quark a ¯nd its antiparticle, the antiquark b. Beauty hadrons can be produced both in e + e -interactions and in hadronic interactions, for instance in p p collisions at 13 TeV at LHC that offers a large cross-section and a full spectrum for beauty mesons and baryons, while electron-positron colliders provide instead an extremely clean environment and a well and coherent initial state Y(4S). The asymmetric e + e - B factory concept at SuperKEKB, uses different energies for the electron and positron beams so that the Y(4S) acquires a boost in the laboratory frame and the decay products are pushed forward in the direction of the electron beam. Figure 5.29 shows an schematic overview of SuperKEKB collider. It consists of two major parts: the linear accelerator and the storage ring which includes the high energy ring (HER) for electrons and the low energy ring (LER) for the positrons. The electrons and positrons were brought to collision at the interaction point (IP), which was surrounded by the Belle II detector. SuperKEKB aims at a peak lumonisity of 8 × 10 35 cm -2 s -1 which correspond to an integrated lu- minosity of 50 ab -1 , 40 times larger then the luminosity produced at Belle as shown in table 3.2. However to reach the designed instantaneous luminosity, several modification were needed, these modifications are listed in more in the following section 3.1.1 as well as in table 3.2.

The event rate for a process with cross section σ can be written

dN dt = L . σ,
where the instantaneous luminosity L for two beams with a gaussian profile of horizontal and vertical size σ x and σ y , is given by:

L = N e + N e -f c 4πσ x σ y . R L ,
where N e + and N e -are the number of particles in a positron and in an electron bunch, f c is the bunch crossing frequency, and R L is a reduction factor accounting for a geometrical effects associated with the finite crossing angle and the bunch length. To increase the luminosity, SuperKEKB increases the beam currents I e + /e -∝ N e -/e + f c by a factor of two compared to KEKB, reduces the beam sizes:

σ x/y (s) = ǫ x/y β x/y (s),
where ǫ is the emittance being a constant of motion along the orbit. β the is the so called "β function " that describes the displacement of a particle beam due to oscillations in the transverse plane xy with respect to its nominal trajectory in a given point (s) along the orbit. To achieve a low emittance, a new damping ring 5.29 was constructed for the positrons in order to cool their transverse momentum since it is easier to achieve a low emittance with a higher energy, the beam energies at SuperKEKB were modified to further reduce the emittance of the positron beam.

Nano-beam scheme

The major new feature in the luminosity upgrade of SuperKEKB is the so-called nano beam scheme, where the vertical β function at the IP "interaction point" called β * y is squeezed down to about 0.3 mm (around 20 times smaller than at KEKB) resulting in a vertical beam size of only σ * y ≃ 60 nm. To achieve the nano beam scheme, the beam crossing angle φ c was increased by about a factor of four compared to KEKB. Figure 3.3 shows a schematic view of the beam crossing at KEKB and at SuperKEKB. At SuperKEKB, the size of the interaction region in z-direction σ z is about 20 times smaller than at KEKB. As stated before, the important running mode of SuperKEKB is at the Y(4S), and due to the asymmetric beam energies, the Y(4S) is produced with a boost βγ. The boost depends on the beam energies and on the crossing angle between them. For a head-on collision, the boost magnitude is given by:

β = p Y(4S).c E Y(4S) = E HER -E LER E HER + E LER , γ = 1 1 -β 2 , βγ = E HER -E LER √ s
The boost βγ is needed to measure the time difference between the decays of the two B 0 mesons produced at the Υ(4S), since ∆t = ∆z/βγ. Due to the reduction of the beam-energy asymmetry at SuperKEKB, the boost is reduced by factor ≃ 2/3 compared to KEKB. Thus, the average distance ∆l (∆z in boost direction) of about 190 µm at KEKB, is reduced to about 130 µm at SuperKEKB. To avoid a deterioration of the ∆t resolution, the new Belle II experiment has a novel vertex detector, as well as improved track and vertex reconstruction algorithms.

The new SuperKEKB upgrades needed to increase the luminosity has a counter effect appearing in the beam-induced background, this type of background is crucial in Belle II and increases relatively with the nano-beam scheme upgrade.

Beam-Induced Background

The tracking detectors presented in 3.3.1, rely on the measurement of the deposited energy of the produced final state particles. Unfortunately, in most of these detectors the number of background-induced energy depositions is equal SuperKEKB and Belle II project or even higher than the number of the ones coming from signal. Thus background hits mimic typical signal hits and pose a severe problem for event reconstruction. Most of these background sources are unique to e+ e-colliders and cannot be seen at proton colliders like LHC experiments.The main beam background sources at SuperKEKB are five.

Tousckek scattering Touschek scattering is highly enhanced due to the nanobeam scheme technique and squeezed beams since it is proportional to the beam size. It is an intra-bunch process which consists in the coulomb scattering of two particles within the same bunch, implying as result a shift in the energies of the particles involved, one getting higher and one decreasing of the same amount, therefore deviating from the nominal energy and from the stable orbit. Fortunately, the rate of Touschek scattering also scales with the beam energy E as E -3 so increasing the energy of the LER compared to Belle is a first countermeasure.

Beam-gas scattering

The interactions of the accelerated bunches with residual gas in the beam-pipe causes bremsstrahlung and Coulomb scattering. This changes the kinematic properties of the beam particles making them deviate from their nominal values. These disturbed particles hit the walls of the beam pipe or the surrounding magnets producing secondary showers of particles, which can leave measurable traces in the detector.

Synchrotron Radiation (SR)

This type is emitted due to the transversal acceleration of the electrons and positrons in the storage ring, the leptons emit synchrotron radiation with high intensity. This is especially the case in the interaction region with its strong focusing magnets. The produced photons have an energy high enough to cause ionization in the detector material of the inner detector layers.

The last two types of beam background are generated during collisions and are luminosity dependent.

Radiative-Bhabha process

The cross section for Bhabha interactions of the accelerated electrons and positrons is much enhanced compared to the one of signal processes. These radiative processes do not only produce collision events, which must be filtered out by the trigger system, but also produce photons and beam particles with non-nominal kinematic properties. The production rate is proportional to the luminosity, therefore it is expected to be 40 times the background level at KEKB.

Electron-Positron Pair Production

The most severe background for the innermost detector layer are low-momentum electron-positron pairs resulting from the two-photon processes in e+ e-→ e+ e-e+ e-reactions. The number of background energy depositions on just the first PXD layer in one readout can go up to 14000 hits with the planned luminosity compared to around ten anticipated Belle II detector signal hits.

SuperKEKB commissioning and running phases

The commissioning of SuperKEKB has been carried out in three phases. In Phase 1 (2016) the accelerator rings have been commissioned without the final focusing system at the interaction point and without the Belle II detector. The main goals were to ensure beam background levels are safe to install Belle II, to provide feedback for the accelerator optimization on how the machine parameters affect background levels and validate the simulation studies on expected backgrounds, which are crucial to reliably estimate detector lifetimes. These goals have been achieved thanks to the BEAST II detectors system [START_REF] Lewis | First Measurements of Beam Backgrounds at SuperKEKB[END_REF], composed of eight sub-detectors devoted to the measurement of many properties of Su-perKEKB backgrounds at the interaction region. During the Phase 2 commissioning (2018), the final focusing and the positron damping ring were in place, together with the Belle II detector, except for the vertex detector, Instead of the final PiXel Detector (PXD) and Silicon Vertex Detector (SVD) (detailed in section 3.3.1 3.3.1), a special cartridge was installed close to the interaction region, which included the BEAST II detectors and one single ladder per each layer of PXD and SVD detectors, a schematic view is provided in Figure 3.5. The goal for such a configuration was double: to commission the machine by measuring beam background rates and providing feedback for accelerator tuning and to ensure the radiation safety of Belle II to run at higher luminosity with the final vertex detector installed, without damaging it. Also, additional collimators to protect the Belle II detector have been installed before the beginning of the data taking. The first physics collisions were detected on April 26 th , 2018. The data taking continued until Ju ly 2018, with a maximum achieved instantaneous luminosity of 5 × 10 33 cm -2 s -1 and a total integrated luminosity of ∼ 0.5 fb -1 as shown in Figure 3.4. These data have been used to prove the understanding of the detector through performance measurements and several rediscoveries. In Phase 3, the full vertex detector has been installed and started taking data with Belle II in March 2019. The application of the final nano-beam scheme will allow to reach the design luminosity and collect in the next ten years 50 ab -1 . Thanks to such a dataset a very rich physics program can be pursued [START_REF] Altmannshofer | Belle-II, The Belle II Physics Book[END_REF], which includes the measurement of time dependent CP violation and CKM parameters with a precision below the current threshold of percent level, hadronic charmless B decays and direct CP violation, charm and quarkonium physics, τ and low multiplicity studies as well as the search for physics beyond the SM through precision measurements.

Belle II detector

The Belle II detector is described in detail in the Technical Design Report [START_REF] Abe | Belle-II[END_REF]. In this section, a general description of each sub-detector is listed. The changes and Belle II detector improvements with respect to the Belle detector are highlighted. In Section 3.3.5 the Belle II trigger system is described, followed by an overview of the software framework developed to analyze the collected data sets Compared to Belle, the Belle II detector will be taking data at an accelerator with a 40 times higher luminosity, and thus has to be able to operate at 40 times higher event rates, as well as with backgrounds rates higher by a factor of 10 to 20 [START_REF] Abe | Belle-II[END_REF]. To maintain the excellent performance of Belle II, the critical issue will be to mitigate the effects of higher background levels, thus the following modification to the Belle II detector design are taken:

Belle II detector

• Inner part of the vertex silicon strip detector, next to the beam pipe, is replaced by a two-layer silicon pixel detector based on DEPFET technology with a very light material budget, these layers are placed at a smaller radius (r L1 = 14, r L2 = 22) then in Belle.

• Silicon strip detector are placed after the pixel detector and occupies a larger radius (140 mm) than in Belle (88 mm), the silicon strips readout is based on APV25 chips which have a shorter shaping time with respect to Belle VA1TA chips to cope with higher background

• Central drift chamber tracking device extends to a larger radius (1130 mm) then Belle (880 mm). It has smaller drift cells than the one used in Belle to be able to operate at high event rates with increased background.

• New particle identification devices, both in the barrel and in the endcaps, are more compact and highly performing, exploiting the Cherenkov image detection method and a very fast readout electronics.

• Electronics of the electromagnetic calorimeter is replaced with a fast waveform-sampling circuit.

• The two layers of the barrel part and in the end-caps of the muon and K L detector, Resistive Plate Chambers (RPCs) are replaced by scintillators readout with wavelength shifting fibers and Silicon Photomultiplier (SiPM). field after a discharge significantly reduces the detection efficiency under such background fluxes.

• New data acquisition system for handling the higher event rate is provided.

These changes will permit a better Belle II performance in several way, especially the vertex resolution improvement due to the two innermost pixel layers, a better reconstruction efficiency for the K S decaying to charged pions, which is crucial for the analysis of the golden mode B → J/ψK s exploited in CP asymmetries measurements. In addition, the new particle identification devices ensure a better pion/kaon separation in the whole kinematics range of the experiment. Finally, a better performing electronics for the calorimeter readout reduces the pile up, improving missing energy measurements. [START_REF] Abe | Belle-II[END_REF], while in the bottom, the longitudinal view of the old Belle detector is shown.

Tracking Detectors

Pixel vertex detector

The PiXel Detector (PXD) [START_REF] Luetticke | The ultralight DEPFET pixel detector of the Belle II experiment[END_REF] concept implemented at Belle II is based on the DEPFET (Depleted Field Effect Transistor) technology which allows to have very thin pixel (50 µm) with readout electronics moved outside the acceptance region covering a polar angle from 17 • to 155 • , therefore reducing the material budget that contributes to the multiple scattering.

DEPFET is a semiconductor detector concept able to combine detection and amplification in one device. A DEPFET pixel consists in a p-channel MOSFET structure integrated onto a fully depleted silicon substrate. The MOSFET has an internal gate where the electrons generated when a charged particle passes through the device are collected. The internal gate modulates the current at readout time allowing the detection of the collected charge.

The DEPFET sensors are organized into planar modules, the ladders, which compose the two layers of the PXD, with radii respectively of 14 and 22 mm. The sensitive lengths of each layer are determined by the acceptance requirements of the detector: a polar angular coverage from 17 • to 155 • ensured. The total amount of pixels composing the PXD is around 8 million organized into arrays. Each DEPFET pixel represents a cell, a monolithic structure with internal amplification, therefore much thinner than other devices which need additional amplification. Pixel sizes have to meet the vertex resolution requirement (20 µm), and the thinning feasibility, resulting in a 50 × 50 µm 2 and 50 × 75 µm 2 cells respectively for the inner and outer layers. Another challenging requirement is the short frame readout time, that is achieved by splitting the readout on both sides of the pixel matrix and introducing high level of parallelization (a four-row simultaneous readout): the processing time for each pixel row is of order 100 ns, and all the 1600 rows can be read in a total frame time of 20 µs. The sensors are finally mounted on the supporting structure which is able to slide on the beam pipe to accommodate for thermal expansion.

Vertex installation in Phase 3

For the early Phase 3 started in March 2019 after the installation of the vertex detector, due to problems in the assembling of the PXD ladders, only half of the designed PXD has been installed, consisting in the full first layer and 2 ladders of the second one. The PXD installation is expected to be finalized in 2021.

Silicon strip vertex detector SVD

The SVD is composed of four layers as shown in Figure 3.9, each SVD layer is composed of ladders of 2-5 DSSD (double-sided silicon strip detector) sensors.

The four layers are called L3-6. Ladders in the outer layers have more sensors to cover the wider acceptance region. To effectively cover the asymmetrically wide acceptance in the forward side, most forward (FW) sensors in L4-6 ladders are slanted towards z-axis. The ladders are placed in a windmill shape to make the edges overlap. To ensure a good performance of the Silicon Vertex detector in Belle II, it requires a very low material budget and short shaping time in order to limit the occupancy.The former issue is solved by adopting the largest possible silicon wafers and equipping the forward region with trapezoidal slanted sensors, while for the latter, the solution came from inheriting the APV25 chips first used in the tracker of the CMS experiment (LHC), equipped with 128 channels each and a shaping time of 50 ns. Moreover, the multi-peak operational mode of the APV25, where six (or three) consecutive samples along the shaping curve are recorded with each trigger, ensures a time resolution of order of 3 ns. The excellent SVD performance results in a innermost layer occupancy smaller than 1 %.

Central Drift Chamber

The central tracking device, surrounding the SVD system, completing the tracking system. The (CDC) has three main functions. It contributes to the reconstruction of charged particles and momentum measurements. Second, It helps in particle identification thanks to the measurements of the energy loss ( dE dx ) due to ionization in the gas volume. Finally, it provides reliable trigger signals for charged particle events. As stated is section 3.3, CDC in Belle II covers a larger radius and has 56 layers of sense wires, 6 more than the Belle CDC.

The CDC is a large gaseous detector (50 % He, 50 % C2H6) composed by 56 cylindrical layers of wires, divided into 9 super-layers. The super-layers alternate between stereo and axial layers; the stereo angles goes from 45 mrad to 74 mrad and is necessary to measure the z coordinate of the tracks. Super-layer are composed of six layers, except for the innermost one which has two additional layers with smaller drift cells to cope with the higher background level. The radial cell size is 10 mm for the innermost super-layer and 18.2 mm for the other super layers. The chamber inner radius is 16 cm while the outer radius is 113 cm, . The CDC provides a position resolution of 2 mm in z and 100 µ m in r. The resolution on the energy loss by a charged particle inside the chamber is 12 %, for incoming particles at θ = 90 • . There are three main structural components of the CDC: a carbon-fiber inner cylinder, two aluminum end plates and a carbonfiber outer cylinder. The two aluminum end plates have complex conical shapes to maximize acceptance avoiding excessive rates coming mainly from Bhabha scattering.

Particle Identification devices

Particle identification is crucial for distinguishing between final state hadrons and leptons, Belle II has a PID system consisting of the TOP (Time Of Propagation counter) in the barrel region and the ARICH (The Aerogel Ring-Imaging Cherenkov counter) detector located at the forward endcap.

Time Of Propagation counter (TOP)

The Time-Of-Propagation counter conceptual overview is shown in Figure 3.10. It consists of array of quartz bars surrounding the outer wall of the CDC divided into 16 modules in φ in the baseline geometry. When a charged particle passes through the quartz bars, Cherenkov radiation is emitted with an angle θ C with respect to the direction of motion of the particle. The cosine of θ C is inversely proportional to the speed of the particle and to the refractive index of the material. Thus Cherenkov photons are emitted at different angles, depending on the mass of the incoming particle. The time of propagation of the Cherenkov photons internally reflected by a mirror at the forward end of the bars, is measured 3.11. The Cherenkov image is reconstructed from the 3-dimensional information provided by two coordinates (x, y) and precise timing, which is determined by micro-channel plate (MCP) PMTs at the end surfaces of the quartz bar.

The PID power is limited by the broadening of the time resolution due to the chromaticity of Cherenkov photons. To minimize the chromatic effect, we introduce a focusing system which divides the ring image according to the wavelength of Cherenkov photons. Figure 3.12 shows the schematic set-up. A focusing mirror is introduced at the end of the quartz bar. The PMT is aligned to measure the position of the photon impact in x and y. The cross section of the quartz bar is a rectangle, we can therefore expand the light trajectory into the mirrorimage region and create a virtual readout screen. The TOP counter requires photo-sensors with a single photon time resolution of about 100 ps, which can be achieved with a 16-channel MCP PMTs specially developed for this purpose. For precision timing required in this type of counter, a custom-made waveform sampling read-out electronics is used. Note that for this identification method the starting (particle production) time has to be known with a precision of about 50 ps; this is indeed challenging, but was already achieved for the time-of-flight (TOF) counter of Belle.

The Aerogel Ring-Imaging Cherenkov counter

In the forward end-cap region, ARICH, a proximity focusing Cherenkov ring imaging detector with aerogel as Cherenkov radiator has been designed to separate kaons from pions over most of their momentum spectrum. It consists of 2 layers of aerogel producing Cherenkov photons, when a charged particle passes through its volume as shown in Figure 3.13, an expansion volume of 20 cm divides the aerogel tile from the photon detector surface and allows the Cherenkov photons to enlarge into rings. The array of position sensitive photon detectors provides single photon detection in a high magnetic field (1.5 T) with optimal resolution in two dimensions.

The main parameters describing the detector are the number of detected photons N γ and the resolution on the Cherenkov angle σ θ . Increasing the radiator thickness, the number of detected photons increases and the resolution per charged track improves as σ θ / N γ , but the angular resolution on the single photon (σ θ ) degrades due to the uncertainty of the emission point. Combining two layers with appropriately tuned refractive indices in order to have two overlapping rings will reduce the spread due to the emission point uncertainty, achieving a resolution on the Cherenkov angle σ θ ≃ 16 mrad. The performance is optimized for charged tracks with momentum larger than 3.5 GeV/c, but no significant degradation is shown also for lower momentum tracks. A non-homogeneous aerogel radiator (Figure 3.13) has been devised, with a global acceptance covering the azimuthal angular region from 15 • to 30 • . The proximity focusing technique is applied by choosing as upstream layer the aerogel with lower refractive index (n 1 = 1.046) and increasing the refractive index of the downstream layer (n 2 = 1.056). Studies have shown that a twice as thick layer of homogeneous aerogel radiator would provide the same number of photons, but with a worse resolution σ θ ≃ 20 mrad. The development of reliable photo sensors with good efficiency for single-photon detection in the high magnetic field is achieved with the Hybrid Avalanche Photo-Detectors (HAPD) by Hamamatsu Photonics. Finally, considering the studies on Cherenkov angle resolution and on average 12.7 detected Cherenkov photons as measured during for Phase 3, the precision achieved is

σ track = σ θ / N γ ≃ 4.5mrad.
In Figures 3.14 and 3.15 show the latest performances of the charged kaon and pion identification based on Phase 3 data. Precisely studies the binary likelihood ratio, defined as, R K/π = L K (L K + L π ). The two figures shows the kaon/muon identification efficiency defined as: These figures shows good performances when comparing data with MC, simulated data.

ǫ K /ǫ π =

Electromagnetic calorimeter

Since the tracking systems can only measure charged particles, an electromagnetic calorimeter (ECL) is needed to measure the energy deposition of the neutral photons using scintillating CsI(Tl) crystals. Neutral π 0 particles are measured via their decay into photons. By measuring the energy and the radiative energy deposition caused by bremsstrahlung for electrons and positrons, additional information is gained for particles which were already reconstructed by the tracking system. In addition, the calorimeter provides luminosity measurements, proper trigger signal generation refsec:trigger and together with the KLM 3.3.4 ensures K 0 L detection. As for the structure of the ECL, a total of 8736 scintillator crystals cover a polar angle range of ∼ 12 • < θ < 155 • , with 6624 and 2112 divided between the barrel and end-caps, respectively. When ionising particles enter the scintillator crystals, their energy is absorbed and re-emitted in the form of photons, which are then detected via photo-diodes glued to each crystal. The same crystals have been inherited for the Belle II ECL, due to only minimal damage received during the run-time of KEKB. At present, the crystals are made of Thallium-activated Cesium Iodide, CsI(Tl), a scintillating material with a considerably large light output. The ECL electronics have also been significantly upgraded since Belle, with major improvements to the readout time achieved.

The neutral kaon and muon detector

Finally, the K 0 L and µ detector, the outermost layer of the detector similarly sectioned into the barrel and endcap regions, is designed for the detection and identification of muons and neutral K 0 L mesons. It is located outside of the superconducting solenoid used to provide the 1.5 T magnetic field to the detector, which occupies the space between the ECL and the KLM, as can be seen in Figure 3.6. The angular coverage of the KLM is comparable to that of the ECL with a ∼ 12 • < θ < 155 • range in polar angle, and polyethylene sheets that shield the KLM from multiple backgrounds including neutrons produced from beam background processes. Resembling closely the successful Belle KLM, detector elements known as resistive plate chambers (RPCs) are wedged between 4.7 cm thick iron plates in the barrel.When hadrons deposit energy into the ECL or collide with the iron plates, they interact strongly such that a characteristic shower of secondary hadrons is produced. These traverse the iron plates and are detected by the RPCs via the charged hadrons present in the shower.Each RPC consists of two parallel electrode sheets made from an insulating substance known as float glass across which a high voltage is applied. Charged particles can ionize the gas between the electrodes, with electrons and ions accelerated to the anode and cathode, respectively. At the end-caps, however, RPCs are no longer optimal when contending with the higher luminosity beam background effects, and polystyrene scintillator strips are used in lieu of the RPCs within both the forward and backward end-caps.

Belle II detector

Much like photons, neutral hadrons including K 0 L mesons cannot be detected by the charged particle tracking sub-detectors, and are only able to deposit energy within the ECL and/or the KLM. Given this, clusters registered only in the KLM, or aligned clusters in both the ECL and KLM that cannot be matched to any charged particle track, strongly indicate the presence of a neutral hadron.

The nature of the momentum of the muons produced at Belle and Belle II is such that the muons are most often low ionizing, and can traverse the ECL and even the iron plates with minimal energy loss. As such, muons produce non-shower hits in the KLM that can be matched to tracks in the CDC. This provides a useful feature for the discrimination between muons and other charged hadrons, particularly pions, that do generate hadronic showers within the KLM. For high-purity samples of muons(for example from the reactions e + e -→ µ + µ -(γ) ), it has been estimated that the barrel section of the KLM provides a µ -reconstruction efficiency of 89 % for particle momenta above 1 GeV/c.

Trigger

Although the number of particles in a single bunch is high, not every collision produces an interesting signature, especially not a B meson decay. The collision rate is dominated by elastic Bhabha scattering processes, which are not of interest for the physics studies performed on the Belle II data. As the high number of those physically uninteresting processes cannot be stored or transported and they are also not needed for later analyses, early filter stages on hardware and software are necessary. Additionally, the detector readout of the sub-detectors needs to be synchronized to make sure that each device records the data of the same collision event. The full readout chain is shown in Figure 3.16 More detailed information is stated in the following sections.

Detector Readout and Hardware Trigger

Belle II's online trigger (also called Level 1 or L1 trigger) system gathers many sub-trigger systems which provide information from various subdetectors, merged by the global reconstruction logic (GRL), whose output is sent to the global decision logic (GDL), responsible for issuing the trigger signal. The first combination of detector information is performed by the GRL and it is mainly based on the drift chamber trigger and on the ECL trigger. The CDC trigger finds and characterizes the tracks detected in the drift chamber. The 2D tracking basically follows the same implementation as Belle. The Belle II CDC detection improvement with the 3D tracking, which adds the information on the z-coordinate, allows to reject the most part of the background coming from Touchshek intra-bunch scattering. In fact, these scattering events show a large displacement in their z-position with respect to the nominal interaction region. The maximum 5 µs latency of the L1 trigger system requires a very fast z-vertex reconstruction, to be performed in no more than 1 µs, which is achieved thanks to neural networks techniques.

Belle II detector

The calorimeter trigger system adopts two complementary trigger schemes: a total energy trigger and an isolated cluster counting technique, the former being sensitive to events with high electromagnetic energy deposition, the latter to multi-hadronic physics events with low energy clusters and/or minimum ionizing particles. Moreover, the ECL trigger is able to recognize the back-to-back topology of Bhabha scattering with a high purity, which is fundamental for ensuring a high trigger efficiency of low multiplicity processes.

The L1 trigger can sustain a maximum instantaneous rate of 30 kHz, however the goal is to keep the trigger rate as low as possible, while ensuring a high efficiency (larger than 99 %) for physics targets, mainly hadronic events. The L1 output is then forwarded to the High Level Trigger for further background rejection based on fully reconstructed objects.

The High Level Trigger

The decision whether to finally keep the event after the software trigger is based on variables calculated on the event topology and the physical properties of the particles. This implies, that the particles are fully reconstructed using the detector data, which is a highly demanding task. This task cannot only be implemented on low-level hardware but needs software running on a server farm. The HLT is a software trigger developed to improve the backgrounds suppression and main purpose to reduce the load of data written on permanent storage at a maximum design output event rate of 10 kHz. Events preselected by using only the information provided by CDC and ECL triggers undergo the full offline reconstruction, involving all output from the subdetectors except the PXD. The physics trigger is then able to classify the event category (B B, e + e -→ τ + τ -, etc.) and once this has been assigned, the HLT processing results containing the event tag and the track parameter estimate are combined with the information from the PXD, which enables to calculate the Region of Interest (ROI), A rectangular-shaped region around the extrapolated positions on each sensor plane, where a particle is expected to travel through the detector. Only the pixels belonging to that region are readout and the selected PXD hits are used to complete the event reconstruction.

During the recording of the collisions, the data needs to be monitored to assure a constant data quality without degradation in neither the detector systems, the triggers nor the online reconstruction. A defined fraction of triggered events together with the PXD information is not only sent to the storage system, but also to the ExpressReco farm, which executes the default offline reconstruction and extracts a set of monitoring plots, which are shown integrated over multiple events to the control room shifters. Software for automatic deviation detection helps to identify possible failures of hardware and software.

Storage and Offline Reconstruction

Belle II detector

The combined subdetector data of the events, that survive the different trigger stages is stored to disk afterwards. Asynchronously to the data taking, the recorded data is reprocessed using a slower but more precise offline reconstruction running on a large computing cluster. During this reconstruction, information on the detector conditions (alignment and calibration constants) during the data acquisition is taken into account. Those constants are calculated on the data itself by using well-known physics processes with a distinct topology that allows to measure e.g. the displacement of the different detector layers among each other. The process of calibration and alignment is repeated regularly on the recorded data and the result is fed into a database, which is both used for the reprocessing of the data as well as for future online software runs. The output of the offline reconstruction is a summary of the reconstructed particles suitable for physics analyses known as mDST. Skimming campaigns sort the data according to their HLT tags and other variables calculated on the reconstructed particles to make physics analyses faster. The reconstructed as well as the raw data is distributed to different computing centers around the world for better accessibility and data backup.

CHAPTER 4

TDCPV Analysis of

B 0 → K 0 S π + π -γ and B 0 → K 0 S π 0 γ
In this chapter, we introduce the Time dependent CP violation of B 0 → K 0 S π + π -γ and B 0 → K 0 S π 0 γ analysis done using Belle II simulated data. The chapter starts by covering the concepts, details, analysis techniques used in the analysis. Then, I present the analysis steps followed to investigate the sensitivity of Belle II to non-zero values of S the two TDCPV channels.

Principle of measurement

In the following section, the main principles used by Belle II are described, this principles have enabled to perform time dependent CP violation measurements.

At Belle II, the electron-positron collisions provide a clean environment for studying B 0 physics. The center of mass energy of colliding electron and positron beams is at the Υ(4S) resonance of 10.58 GeV which decays to a B 0 B 0 pair and this pair is practically at rest in the Υ(4S) center of mass system (CMS).

The B 0 B 0 meson pair is produced in a quantum coherent state (quantum entangled). When propagating, each B meson undergoes flavor mixing. But the pair coherence insures that if one meson changes flavor, the other automatically changes flavor too. Hence, the opposite flavor is preserved within the pair until one meson decays. This fact allows the so-called flavor tagging technique. In this analysis, we note one of the meson B 0 tag , to decay at time t tag into a flavor specific final state, experimentally identified through inclusive reconstruction. By quantum entanglement we know that the other B meson of the pair, noted in this analysis B 0 sig , was in the opposite flavor eigenstate at the same time t tag . Then as B 0 sig evolves in time, it decays into the states of interest B 0 → K 0 S π + π -γ and B 0 → K 0 S π 0 γ at t tag + ∆t, B 0 sig could decay before B 0 tag decays, resulting in negative ∆t. In order to infer ∆t, the distance between the decay vertices of B 0 tag and B 0 sig is measured benefiting from the asymmetric colliding beam energies.

TDCVP Analysis of B 0 → K 0 S π + π -γ and B 0 → K 0 S π 0 γ
At SuperKEKB collider, the electron beam energy is 7 GeV, while the positron beam energy is 4 GeV. The resulting Υ(4S) resonance is boosted along the beam direction 1 with a boost factor βγ = 0.28. The already mentioned fact that a B 0 meson pair is practically at rest in the Υ(4S) center of mass frame, allows to derive the following conversion between the time difference ∆t and the distance between the two B 0 decay vertices ∆z:

∆t ≃ ∆z γβc , ( 4.1)
Taking into account the known value of the B meson lifetime τ B 0 ∼ 1.5 ps, ∆z is about 136 µm. The z vertex position is related to the proper time t by:

TDCVP Analysis of B 0 → K 0 S π + π -γ and B 0 → K 0 S π 0 γ z = γ(α cos θ + β 1 + α 2 )ct (4.2)
where γ and β are the boost parameters from the Υ(4S) frame to the lab frame and θ and α = p * B c/m B c 2 are the polar angle and boost factor of the B in the Υ(4S) frame. Since no tracks originate from the production vertex, the sensitivity to the decay time difference of the B 0 mesons comes mainly through the difference in the z positions of the decay vertices. As the polar angles of the two B mesons are exactly opposite, the difference in the z positions can be expressed as

∆z = γβ (1 + α 2 )c(t 1 -t 2 ) + γα cos θ c (t 1 + t 2 ). (4.3)
since the parameter α ∼ 0.06, it is ignored, and one obtains the well known approximation in eq 4.1. Consequently, the experimental resolution on the B meson decay time-difference is dominated by the resolution on the decay vertex position. To measure the time dependent CP violation ∆z has to be determined with the resolution of about 136 µm, or better. Belle II targets 60 µm for this resolution, thanks to the pixel layers of the VXD 3.7.

The described principle of measurement is summarized in Figure 4.1. It can be summarized by four main steps:

1. Determine (by tagging) the flavour of one of the B mesons (B 0 tag ).

2. Reconstruct the associated B 0 sig decaying into either

B 0 → K 0 S π + π -γ or B 0 → K 0 S π 0 γ. 3.
Measure the distance between the decay vertices of B 0 tag and B 0 sig . 4. Extract the TDCPV parameters from the obtained decay time distribution.

The principle presented in the previous section is promising, but the real world is not ideal. Each step requires method and tool that is discussed in the following text.

Flavor tagging

As discussed before, flavour tagging is required for the measurements of CP violation, where the decay of B 0 sig is fully reconstructed and the flavour of the other B 0 meson, B 0 tag has to be determined. The task of the flavour tagger is to determine the flavour of B 0 tag at the time of its decay. The algorithm used is common to most of Belle II measurements and is described in detail in [START_REF] Altmannshofer | Belle-II, The Belle II Physics Book[END_REF]. Since B 0 mesons exhibit a large number of possible decay channels, many of them provide unambiguous flavour signatures through flavour-specific final states. Flavour signatures correspond to signed characteristics of the decay products that are correlated with the charge sign of the b-quark in the B meson. Because of the wide range of possible decay channels it is not feasible to fully reconstruct

TDCVP Analysis of B 0 → K 0 S π + π -γ and B 0 → K 0 S π 0 γ
a large fraction of flavour-specific B 0 tag decays. Instead of a full reconstruction, the flavour tagger applies inclusive techniques based on multivariate methods to maximally exploit the information provided by the different flavour-specific signatures. The Belle II flavour tagger was developed by using several useful concepts of previous algorithms used by the Belle and the BaBar collaborations [START_REF] Bevan | The Physics of the B Factories[END_REF].

Tagging categories

Flavour tagger is based on flavour-specific decay modes with relatively high branching fractions > 2 %). Each decay mode exhibits a particular decay topology and provides a flavour-specific signature. Some additional signatures are obtained by combining similar or complementary decay modes. Within a socalled category, a particular flavour signature is considered separately. The current flavour tagger is based on 13 categories which are presented in

+ Kinetic lepton l - Intermediate Kinetic lepton l + Kaon K - Kaon-Pion K -, π + Maximum P * (CMS) l -, π + Fast-Slow-Correlated (FSC) l -, π + Fast Hadron π + , K - Lambda Λ Table 4.1:
Tagging categories and their targets(left) with some characteristic examples of the considered decay modes (right). l ± stands for charged leptons (µ or e).

The flavour-specific final state particles in the considered decay modes are treated as targets since their charges are correlated with the flavour of B 0 tag . In order to extract these flavour-specific signatures, the targets have to be identified among all available particle candidates. To accomplish this task, discriminating variables are calculated for each particle candidate. An overview of the discriminating variables for each category is presented in details in [START_REF] Altmannshofer | Belle-II, The Belle II Physics Book[END_REF]. The Flavor tagger algorithm combines the results of all categories and tracks considered, and returns two parameters, flavour tag q, and flavour dilution factor r. The output y with a range between 0 and 1, is equivalent to y = q.r, where y = -1(1) if B 0 tag is perfectly tagged as B 0 (B 0 ) respectively.

A schematic overview of the information flow in the algorithm is presented in Figure 4.2. The algorithm has an event-and combiner-levels. The event-level process is performed within each individual category. On this level, a multivariate method based on Fast boosted decision tree (FBDT) [START_REF] Keck | FastBDT: A speed-optimized and cache-friendly implementation of stochastic gradient-boosted decision trees for multivariate classification[END_REF] assigns to each The event-level process is performed within each individual category. Then to each particle candidate a probability y cand is assigned, then combined to provide the final q.r output.

TDCVP Analysis of B 0 → K 0 S π + π -γ and B 0 → K 0 S π 0 γ
particle candidate a probability y cat , which is the probability of being the target of the corresponding category providing the correct flavour tag. Beside q and r the fraction of wrongly tagged candidates (w), called mistag probability and the difference in fraction of wrongly tagged B 0 and B 0 candidates (∆w), is also needed for the TDCPV analysis. The categories are characterized by their average efficiencies ǫ as well as the effective tagging efficiency defined as Q = ǫ(1 -2w) 2 .

Performance

The performance of the Belle II flavour tagger has been evaluated using Belle II simulated data, and real data. Also an comparison between both Belle II simulated and real data with Belle provides interesting insight to assess Belle II's performance. The output y = q.r, which corresponds to the product of tagged flavour q and the dilution factor r, can be found in Figure 4.3 (left) for the FBDT TDCVP Analysis of B 0 → K 0 S π + π -γ and B 0 → K 0 S π 0 γ combiner on MC. Figure 4.3 (right) also shows a linearity check between the true dilution r MC determined using MC information and the mean r of the dilution provided by the combiners. The mean dilution r of the combiner output is simply the mean of |q.r| for each r-bin. Thus Figure 4.3(right) shows the results of the linearity check for events where B 0 tag is a B 0 , for events where B 0 tag is a B 0 , and in average. The FBDT combiner achieves a total effective efficiency ǫ e f f of (36.67 ± 0.5)% on Belle II MC and 34.26 ± 0.03% on Belle MC. Where

ǫ e f f = ∑ i ǫ i .(1 -2w i ) 2 (4.4)
ǫ i is the partial efficiencies(in each r-bin) and w i is the wrong-tag fractions.

In comparison with previous Belle flavour tagger, which reached an effective efficiency of (30 ± 0.4)% on Belle data [START_REF] Bevan | The Physics of the B Factories[END_REF], the Belle II flavour tagger reaches an effective efficiency of (33 ± 0.5)% on Belle data. An additional increase of about 3% in effective efficiency is observed due to the improved track reconstruction and the improved PID performance at Belle II. In

Extraction of CP violation parameter

To extract the values of the CP parameters, A and S, neglecting the experimental effects, the following probability density function (PDF), obtained from the decay rates in equation 2.45 is used to fit the time distribution,

P (∆t, q) = e -|∆t|/τ B 0 4τ B 0 [1 + qA cos(∆M∆t) + S sin(∆M∆t)] (4.5)
where q = +1 when B 0 tag = B 0 and q = -1 when B 0 tag = B 0 . Indeed, in order to obtain correct S and A, we need to include the experimental effects, Equation 4.5 may be re-written in term of the tagging information as:

P (∆t, q) = f sig e -|∆t|/τ B 0 4τ B 0 [1 -q∆w + (1 -2w)qA cos(∆M∆t)+ S sin(∆M∆t)] ⊗ R sig (∆t) -(1 -f sig )P bkg (∆t) (4.6)
where P bkg (∆t) is the PDF describing ∆t distribution of background candidates, and R sig (∆t) ∆t resolution function for signal candidates. In order to obtain unbiased values of CP parameters, it is important to have good understanding and estimations of f sig , w, ∆w, R sig , and P bkg . Then we construct a likelihood function and maximize it to get the best estimates for A and S. TDCVP Analysis of

TDCVP Analysis of B 0 → K 0 S π + π -γ and B 0 → K 0 S π 0 γ
B 0 → K 0 S π + π -γ and B 0 → K 0 S π 0 γ

Preparation of measurement procedure

In this section, the analysis procedure is described in detail.

Data samples

Signal MC: dataset of simulated signal events, where Υ(4S) → B 0 B 0 process, with one B 0 meson decaying to

B 0 → K 0 S π + π -γ or B 0 → K 0 S π 0 γ.
Generic BB MC: dataset of simulated events containing Υ(4S) → B + B -or B 0 B 0 process, with both B mesons decaying generically excluding the signal decay. These events are treated as background in this analysis.

Continuum MC: dataset of simulated continuum events e + e -→ qq (q = u, d, s, c).

No B mesons are produced in these events and they are also background for this analysis.

Full MC: dataset of simulated events obtained by merging signal MC, generic B 0 B 0 MC and continuum MC with fraction as expected in data according to specific luminosity.

B

0 → K 0 S π + π -γ and B 0 → K 0 S π 0 γ decays
The branching fraction of the decays B 0 → K 0 S π + π -γ and B 0 → K 0 S π 0 γ taken from [START_REF] Amhis | Heavy Flavor Averaging Group, Averages of B-Hadron, C-Hadron, and tau-lepton properties as of early 2012[END_REF] [START_REF] Beringer | Particle Data Group, Review of Particle Physics (RPP)[END_REF] are

B(B 0 → K 0 S π + π -γ) = 6.47 × 10 -6 , B(B 0 → K 0 S π 0 γ) = 9 × 10 -6 . (4.7)
B 0 → K 0 S π + π -γ decays through several kaonic resonances called X d which contain also non-CP eigenstates, while B 0 → K 0 S π 0 γ goes through several kaonic resonances and K * 0 that contain only CP eigenstates which make it more sensitive to TDCPV measurement.

Reconstruction and selection cuts

In this section we describe the reconstruction of the two decay channels and the criteria used to reduce the number of B 0 candidates coming from the background events.

For candidate selection, a skim is first applied, as will be described in 4.3.1. After skimming, several cuts are used 4.3.2. At first order, the candidate selection for the present analysis relies on the selection criteria from the previous BABAR and Belle analysis, then this criteria is optimized. For B 0 → K 0 S π + π -γ, we reconstruct X sd → K 0 S π + π -, where K 0 S → π + π + . As well as for B 0 → K 0 S π 0 γ, we reconstruct K 0 S → π + π -and π 0 → γ γ. Therefore, each of the two decay

TDCVP Analysis of B 0 → K 0 S π + π -γ and B 0 → K 0 S π 0 γ
modes is reconstructed by combining the event charged pion tracks and photon candidates, as these are the only final state particle species in our decay. Blindly combining particles would be useless, since there is an abundance of events containing charged tracks and photon hits. Thus we impose the selection criteria that will be satisfied by a large fraction of signal candidates, and at the same time reject a significant amount of background candidates. Having a large amount of background candidates, even if correctly described in the PDF used for the fit, results in a lower sensitivity to the fitted parameters (larger statistical uncertainty). On the other hand, since there is no distribution in which the signal and background candidates are completely separated, by imposing the selection criteria we are also loosing some fraction of signal candidates. Because the goal of this analysis is to obtain the values of TDCPV parameters with the smallest possible uncertainty, we optimize the selection criteria to achieve this goal.

Skim

In order to reduce the size of the data sample and hence gain in processing time, a skim is applied before any other selection criteria. It consist of loose requirements, which can be used by various analysis. In the present analysis, we use the TDCPV skim available in the Belle II collaboration. This skim selects events passing the filter that requires at least three tracks. The skim also requires highenergy photon, consistent with a radiative B decay, and that the CM energy of the highest-energy photon candidate in the event falls between 1.5 and 3.5 GeV.

Selection cuts

High-energy photon selection

The high-energy photons, which are taken from the the loose standard photon lists and further required to pass the following selection criteria:

• 0.3 < θ γ < 2.6
, where θ γ is the polar angle in radians.

• Photon Energy 1.7 < E < 4 GeV.

π ± and π 0 selection

The π ± are selected from the standard pion list in Belle2 software, with no additional cuts, For π 0 , the two photon are required to have an energy > 0.08, and an invariant mass 0.124 < M < 0.140.

Reconstruction of K 0

S

To reconstruct the K 0 S two charged pion tracks are combined, they are chosen from the K 0 S default list with a PID cut larger then 0.005. The geometric fit performed by "TreeFitter" that determines the K 0 S decay vertex, allows to evaluate the K 0 S candidate four momentum and trajectory. Its mass is also computed using π + π -track momenta evaluated at the vertex. In order to determine the trajectory, the K 0 S production vertex (i.e. the B decay vertex) is also required. The displaced decay of the K 0 S is useful for rejecting background, especially qq events. Thus, we compute the decay length significance,

TDCVP Analysis of B 0 → K 0 S π + π -γ and B 0 → K 0 S π 0 γ
d K 0 S /σ(d K 0 S
), defined as the ratio of the three dimensional length of the K 0 S trajectory divided by the error on that quantity obtained from the vertex fit. We also compute θ f light corresponding to the angle between the K 0 S trajectory and its momentum vector. The following cuts are applied on K 0 S candidates:

• |m π + π --m K 0 S | < 11 MeV/c • cos θ f light > 0.995 • d K 0 S /σ(d K 0 S ) > 9
These cuts are chosen first from Belle and Babar analysis but their values have been optimized for the present analysis as discussed more in section 4.3.5 ∆t and σ ∆t Very loose cuts are applied to the variables ∆t and σ ∆t . These cuts were first taken from previous B 0 → K 0 S π + π -γ analysis and then demonstrated using Belle II simulated data. The two distributions are shown in Figure 4.5 and the cuts follows :

• |∆t| ≤ 20 ps • σ ∆t ≤ 2.5 ps TDCVP Analysis of B 0 → K 0 S π + π -γ and B 0 → K 0 S π 0 γ m ππ and m Kππ
In order to increase the proportion of B 0 → K 0 S π + π -γ we apply cuts on the m ππ as well, we restrict the K 0 S ππ resonance mass to be below 1.8 GeV/c 2 , since it is not expected to contain a large number of signal events, while significant number of background events.

• 0.6 GeV/c 2 ≤ m ππ ≤ 0.9 GeV/c 2 ,

• m Kππ < 2 GeV/c 2

Vetos of π 0 and η

As in our signal mode we have a high energy photon, most of our photon background originates from misreconstructed π 0 and η. Indeed, these fake isolated photons either come from asymmetric decays of π 0 and η (one of the photons takes most of the energy of the decaying particle) or from merged photons (the decaying particle has a high momentum in the CM frame therefore the two outgoing photons cannot be properly separated in the EMC). To reduce these backgrounds, the photon candidate γ 1 is associated with all other photons γ 2 . Then we construct the π 0 and η likelihood functions, defined as

LR = p(m γ 1 γ 2 , E γ 2 |θ) p(m γ 1 γ 2 , E γ 2 |K 0 S π + π -γ) + p(m γ 1 γ 2 , E γ 2 |θ) (4.8)
where θ is either the π 0 or η hypothesis, and p is a probability density function in terms of m γ 1 γ 2 and the energy of γ 2 in the lab frame, E γ 2 . The LR of π 0 and η is between zero and one, and the larger the value is, the more likely it is that γ 1 comes from the π 0 or η decay. We select then respectively:

• For B 0 → K 0 S π + π -γ: LR π 0 < 0.82 and LR η < 0.954. • For B 0 → K 0 S π 0 γ: LR π 0 < 0.84 and LR η < 0.91. These cuts where optimized using the procedure described in Section 4.3.5.

Reconstruction of B 0 meson

Taking advantage of the well know initial state, e + e -, at B Factories, combined with the fact the bb pair is produced via the decay of the Υ(4S) resonance, two kinematical variables can be constructed in order to discriminate signal from continuum and generic B 0 B 0 events. Namely, these two variables are the energy difference ∆E and the energy-substituted mass M bc . As well a variable based on the event shape to separate signal from background.

The energy difference ∆E

The energy difference, ∆E, can be expressed in a Lorentz invariant form as

∆E = (2q B q 0 -s)/2 √ s, ( 4.9)
TDCVP Analysis of B 0 → K 0 S π + π -γ and B 0 → K 0 S π 0 γ where q 0 = q + q = (E 0 , p 0 ) are the Lorentz vectors representing the of the initial e + e -system,and q B represents the momentum of the B-meson system and √ s = 2E * beam denotes the CM energy. In the CM frame, ∆E can be expressed as

∆E = E * B - √ s/2, ( 4.10)
where E * B reconstructed energy of the B candidate without applying any constraint. Since ∆E is by construction related to the mass hypotheses for each of the tracks, its distribution will strongly depend on the nature of the final state particles. For instance, in the case where a kaon is misidentified as a pion, its reconstructed energy, and consequently that of the B candidate, will be smaller than expected, and the event will be shifted towards negative values of ∆E. On the other hand, the distribution for correctly reconstructed signal events will peak at zero. This makes ∆E especially helpful in isolating backgrounds from misreconstructed B decays. Moreover, since continuum events do not originate from B decays, their distribution in this variable is expected to be linear in the whole dynamical range, excluding acceptance effects and phase space.

The energy-substituted mass M bc

The momenta of the

M bc = E * beam -p * 2 B (4.11)
where p * 2 B is the CM momentum of the B candidate. Since the candidate is formed from a number of tracks and neutral objects whose energies are not as accurately measured as are the beam conditions, the B-candidate energy is here substituted by E * beam . This allows to improve the mass resolution by using our knowledge of the initial kinematics. Due to the annihilation of the electron and the positron, which creates a BB pair, and to the fact that the masses of the particle and of the antiparticle are equal, for signal events, M bc yields the mass of the B 0 meson and shows a clean peak. Thus we select respectively candidates with:

• For B 0 → K 0 S π + π -γ, M bc > 5.2 GeV/c 2 and |∆E| < 0.2 GeV • For B 0 → K 0 S π 0 γ, M bc > 5.
2 GeV/c 2 and -0.25 < ∆E < 0.2 GeV Figure 4.6 illustrates the discriminating power of these two variables.

Event-shape variables

As already stated in 4.3.3, a strong variable based on the event shape is used to separate signal event from continuum events, since due to the kinematics of the decay products in e + e -→ Υ(4S) → BB and e + e -→ qq, q = u, d, s, c processes, strong differences arise in the angular correlations among the BB decay daughters and continuum events. BB events follow the spin-1 Υ(4S) resonance decay into two spin-0 B mesons, resulting in a sin 2 θ distribution, where θ is the angle between the B direction and the z-axis. While in continuum events, a small amount of the initial energy is invested in the rest masses of the quarks. As a result most of the available center-of-mass energy will be carried as kinetic energy, which implies that the event will have a two-jet-like structure and will roughly follow a (1+cos 2 θ) dependence, where θ is the center-of-mass angle of a jet with respect to the beam axis. Taking advantage of these differences, several variables discussed below are useful to separate between these two event species.

TDCVP Analysis of B 0 → K 0 S π + π -γ and B 0 → K 0 S π 0 γ

Thrust Axis

The thrust of an ensemble of particles is defined as the direction, t, in which the sum, T, of the projections of the momenta of the particles is maximized:

T = max ∑ i | ti .p * i | ∑ i |p * i | (4.12)
where the index i runs over all the particles in the ensemble. For BB events, T takes almost random values, as the events are mostly isotropic as shown in Figure 4.7. For qq events, on the other hand, T follows the direction of the formed jets, and is therefore strongly directional.

Thrust angles

Employing the thrust axis, several other variables can be employed, such as the cosine of the angle between the thrust axis of the momenta of the B candidate and the z axis, cos θ T, or the cosine of the angle between the thrust axis of the B candidate and the rest of the event, cos θ ROE T . For a BB event, decay particles are isotropically distributed and their thrust axis are randomly distributed. Therefore, cos θ ROE T follows a uniform distribution in the range [0, 1], while for cos θ T, it is uniformly distributed. In contrast, for qq events, the thrusts of both the B TDCVP Analysis of B 0 → K 0 S π + π -γ and B 0 → K 0 S π 0 γ

CLEO Cones

The CLEO collaboration introduced variables based on the sum of the absolute values of the momenta of all particles within angular sectors around the thrust axis, resulting in 9 concentric cones []. The cone in the direction of the thrust axis is merged with the respective cone in the opposite direction. There are two options for constructing the CLEO cones in Belle II, they can be calculated from all final state particles in the event, or from only ROE particles.

Fox-Wolfram moments

For a collection of N particles, the Fox-Wolfram moment H L is defined as

H L = N ∑ i,j |p i ||p j |P L (cos θ i,j ), (4.13)
where p i and p j are the momenta of the i th and the j th particle in the event, P L is the l th order Legendre polynomial and θ ij is the angle between the momenta of particles i and j. The ratio between the 2-nd and 0-th R 2 = H 2 /H 0 , order moments of the rest-of-event is used to describe the event topology in e + e -collisions and presents a strongly discriminating variable. In the case of a qq event, R 2 are expected to be closer to 1, which indicates a jet-like event. In contrast, for BB events, values of R 2 are expected to be closer to 0, indication of a nearly isotropic event.

Modified Fox-Wolfram moments

The Belle II collaboration has also developed the modified Super-Fox-Wolfram moments H so xl and H oo l (l ∈ [0, 4]), where all reconstructed particles in an event are divided into two categories: B candidate daughters (denoted as s) and particles from ROE (denoted as o). The H so xl moments are decomposed into an additional three categories (denoted as x) depending on whether the particle is

TDCVP Analysis of B 0 → K 0 S π + π -γ and B 0 → K 0 S π 0 γ charged (x = c), neutral (x = n), or missing(x = m).
Additionally, for H so xl , the missing momentum of an event is treated as an additional particle.

H so xl = ∑ i ∑ jx |p jx |P l (cos θ i,jx ), (4.14)
where i runs over the B daughters; jx runs over the ROE in the category x; p jx is the momentum of the particle jx; and P l (cos θ i,jx ) is the l th order Legendre polynomial of the cosine of the angle between particles i and jx.

Fisher discriminant

Since the event-shape variables described above exploit different aspects of the same physical principle, some correlations might appear among them. Thus Fisher discriminant (put ref) is constructed taking into account the correlations between them, defined as a linear combination of several discriminating variables x i , taking the advantage of all of them to maximize the separation power.

F = ∑ i a i x i = a T x, (4.15)
where a T is a line vector. The parameter a i are optimized with the use of the signal and continuum simulated data to give the best separation between candidates from true B 0 decays and from the continuum events.

In the current analysis a multivariate analysis (TMVA) is trained using as inputs the thrust, Cleo Cones, and Fox-Wolfram moments variables and produces as a output the Fisher discriminant variable called "CSMVA" that varies from 0 to 1 depending on whether the event is continuum-like or BB-like.

Vertex selection

The B 0 candidates are formed by fitting the vertex of all the final state particles, using tracks or cluster information in case of charged particles or the photon respectively. The fit on the decay products of the reconstructed B 0 → K 0 S π 0 γ is performed with a "iptube", constrained to be on the IP, tube along the tag B line of flight. while no constraint is done for the B 0 → K 0 S π + π -γ. Although the high-energy photon is included in the fit in order to get higher constraints on the B candidate kinematics, it will not contribute to the vertex information.

In order to reduce combinatorial backgrounds, a cut on the vertex probability, which results from the vertex fit, is applied. From the optimization procedure, described below, we select candidates with a vertex probability greater than 0.0001.

TDCVP Analysis of B 0 → K 0 S π + π -γ and B 0 → K 0 S π 0 γ

Cuts Optimization

B 0 → K 0 S π + π -γ cuts optimization Table 4.6 shows all the selection cuts used in the analysis. In order to maxim ize the sensitivity on the CP asymmetry parameters S and C, cut optimization is done by maximizing the Significance, called Figure of merit. This significance defined as S √ S+B

, where S is the signal yield, signed as truth matched in the simulated data and B denotes the background, the total yield signified as nontruth matched in belle II software. The optimization procedure was done inside the signal region (i.e. in M bc > 5.26 GeV/c 2 and-0.2 < ∆E < 0.1), using a set of eight variables,

• m Kππ , LR π 0 , LR η , B vertex probability

• cos θ γ , K 0 S decay length significance • π 1 PID, π 2 PID

Steps

• First for each variable, the significance S ) > 9 is only applied, then the cut with 2 nd highest Significance ranked in step 2, LR π 0 < 0.71 is varied to reach a higher significance, thus for LR π 0 < 0.82 we obtain S √ S+B = 20.46. Then we fix the value of the cut, LR π 0 < 0.82 and vary the the 3 rd ranked cut to get a highest Significance again. Similarly done for the rest of variables.

• In the last step, all the optimized cuts after step 3 are applied, again expect the first ranked cut in step 2, [START_REF] Albrecht | ARGUS, Observation of B0 -anti-B0 Mixing[END_REF] and vary it again to obtain a max significance. In this step, approximately the cut values remain the same for the same highest significance. After all, a S √ S+B 20.9 is reached in the signal region. In addition, test is done on the range of ∆E and Fisher discriminant F , where the fitted errors of the CPasymmetry parameters are compared for ∆E ∈ [-0.2, 0.2] and F > 0.3, 0.2, 0.1, 0 and it showed that the range chosen for ∆E and F > 0 is a good choice and compromise between background suppression and CP parameters. x < 1.8

(d K 0 S /σ(d K 0 S ) >
TDCVP Analysis of B 0 → K 0 S π + π -γ and B 0 → K 0 S π 0 γ
LR π 0 x <0.82 LR η x< 0.954 B vertex probability x>0.0001 ∆E ( GeV) -0.2 x 0.2 m ES ( GeV/c 2 ) 5.2 < x Fisher x > 0.0 B ∆t (ps) -20 x 20 B σ ∆T (ps) x < 2.5 cosθ γ -0.65 x 0.85 |m π + π --m K 0 s | ( GeV/c 2 ) x < 0.011 cosθ f light 0.995 < x d k 0 s /σ(d K 0 s ) x > 9 π 1 PID π 1 PIDpi > 0.34 π 2 PID π 2 PIDpi > 0.34 m π + π -(ρ 0 (770)selection) ( GeV/c 2 )
0.6 x 0.9

B 0 → K 0 S π + π -γ TDCVP Analysis of B 0 → K 0 S π + π -γ and B 0 → K 0 S π 0 γ Cut Value LR π 0 x < 0.84 LR η x< 0.91 ∆E ( GeV) -0.25 x 0.2 m ES ( GeV/c 2 ) 5.2 < x Fisher x > 0.0 B ∆t (ps) -20 x 20 B σ ∆T (ps) x < 2.5 cosθ γ -0.6 x 0.85 |m π + π --m K 0 s | x < 0.016 M K s π0 ( GeV/c 2 ) x < 1.2 d k 0 s /σ(d K 0 s ) x > 5 π 1 PID π 1 PIDpi > 0.34 π 2 PID π 2 PIDpi > 0.34 Photons Energy from π 0 ( GeV)
x > 0.04

Table 4.3: List of the selection cuts used for B 0 → K 0 S π 0 γ B 0 → K 0 S π 0 γ

cuts optimization

The method used to optimize the cuts for B 0 → K 0 S π 0 γ channel is the same used for B 0 → K 0 S π + π -γ, where in the signal region (i.e M bc > 5.26 GeV/c 2 and -0.2 < ∆E < 0.1) the cut with highest S √ S+B = 20, LR π 0 < 0.8 is optimized as well as all the cuts used for B 0 → K 0 S π 0 γ selection from table 4.3, expect M bc , ∆E, ∆t, σ ∆t and CSMVA. After the same full optimization method, a S √ S+B = 20.6 is reached.

Cuts Optimization result

As will be shown in the next section, a four dimensional fit to M bc , ∆E, ∆t and Fisher is done to extract the CP parameters S and A. This fit has been done before and after the optimization of the cuts. The final result shown in section 4.4 shows the results using the optimized cuts. These results of the CP parameters statistical uncertainties have been decreased by 10% of their values after fitting using the optimized cuts.

Multiple candidate selection

To select a single candidate in each event where more than one is reconstructed and passes the selection criteria, χ 2 the "B-vertex-probability" cut is used to select the best candidate. The technique is mainly carried out by ranking the candidates for each event according to their probability, then choosing the best candidate corresponding to the best χ 2 ). This method is used for both TDCPV channels.

TDCVP Analysis of B 0 → K 0 S π + π -γ and B 0 → K 0 S π 0 γ

Fit to M bc , ∆E, ∆t and Fisher

In this section, we present the fit performed on M bc , ∆E, the Fisher discriminant and ∆t in order to extract the CP asymmetry parameters of the signal. The section 4.4.1 and 4.4.2 detail the PDFs used in the fit model for the signal and background categories, respectively. Same PDFs are used in both channels, In section 4.4.4 gives the CP asymmetries extracted by the fit.

Signal PDFs

PDFs for truth matched signal events are constructed using the signal MC sample, where the M bc PDF, P M bc is described by a Crystal Ball function, the ∆E PDF, P ∆E by also a Crystal Ball and the Fisher discriminant, P CS by sum of two Crystal Ball functions. The ∆t signal PDF is defined in 5.7, where ∆t resolution R sig (∆t) is modeled by three Gaussians.

Background PDFs

Here we present the probability density functions of the two background categories, BB background and continuum background. The same functions have been used for both channels, while parameters extracted from the individual fits to each contribution changes and get fixed in the final four dimensional fit.

Starting with the BB background, the M bc PDF, P BB M bc is described by a sum of a gaussian and argus functions. ∆E PDF, P BB ∆E by a first order chebychev function. The Fisher discriminant, P BB CS by a Crystal Ball. The ∆t BB background PDF is described by a sum of three Gaussian distributions. The continuum P cont M bc is modeled by an Argus function, ∆E P cont ∆E by Chebychev function and P cont CS by a Gaussian. The ∆t BB background PDF is described by a sum of three Gaussian distribution.

Signal to background fraction fit

In order to fit the CP violation parameters, the four dimensional fit, requires estimation of the fraction of the signal candidates among all candidates reconstructed in the full simulated data. First as discussed above, we model the distributions of signal and background candidates for M bc and ∆E, where the specified models are used in this fit. Then we build a PDF as a sum of these two models

P(M bc , ∆E) = f sig P sig (M bc , ∆E) + (1 -f sig )P bkg (M bc , ∆E) (4.16)

Results

In this section, we present the projections and CP violation parameters obtained from the four-dimensional fit already presented above. Figure 4.10 and 4.9 shows the projection of fit on each of M bc , ∆E, ∆t and CSMVA for the both B 0 → K 0 S π + π -γ and B 0 → K 0 S π 0 γ channels. The full PDF used in the fit is as follows:

TDCVP Analysis of B 0 → K 0 S π + π -γ and B 0 → K 0 S π 0 γ
P f ull = f sig P sig (M bc , ∆E, ∆t, CSMVA) + (1 -f sig )[ f BB P b (M bc , ∆E, ∆t , CSMVA) + (1 -f BB )P cont (M bc , ∆E, ∆t, CSMVA)] (4.17)
where f sig is the fraction of the signal events in the sample, it is calculated using two dimensional fit of M bc and ∆E. f BB is the fraction of the BB events, it is fixed in the final fit using also the 2D fit. P sig is the four dimensional pdfs of the signal M bc , ∆E, CSMVA, ∆t obtained as a product P sig (M bc , ∆E, ∆t, CSMVA) = P sig (M bc ) × P sig (∆E) × P sig (∆t) × P sig (CSMVA) (4.18) the same form takes the BB pdf background P BB and continuum P cont . The CP violation parameters appear in P sig (∆t) defined in 5.7, where in P f ull A and S are left free, while all other parameters are fixed from simulated data, plus some other parameters left free to account possible difference between data used in the final fit and simulated one. The fitted CP violation parameters are shown in table 4.4.

TDCVP Analysis of B 0 → K 0 S π + π -γ and B 0 → K 0 S π 0 γ

Parameter Value

S B 0 →K 0 S π + π -γ -0.09 ± 0.2 A B 0 →K 0 S π + π -γ -0.21 ± 0.17 S B 0 →K 0 S π 0 γ 0.02 ± 0.30 A B 0 →K 0 S π 0 γ 0.03 ± 0.19
TDCVP Analysis of B 0 → K 0 S π + π -γ and B 0 → K 0 S π 0 γ 4.5 Systematics B 0 → K 0 S π 0 γ
One of my main contributions to the TDCPV analysis, in addition to the cuts optimization is the systematic study. Several sources need to be studied in order to measure the expected systematic uncertainty on the fitted CP violation parameters S and A. In this section, the different sources are listed and discussed as follows and then finally summarized in table 4.5.

• Flavor tagging: In order to take into account the systematics due to flavour tagging, the parameter dw, the fraction of wrongly tagged candidates is varied by 0.1 %.

• Fitting procedure: Several parameters are fixed in the four dimensional fit done using P all , we need to take into account the possible effects of fixing these parameters, thus they are varied by 1 sigma, where sigma is the error taken from the separate fits done to model each distribution component.

Eor each varied parameter, the difference between the nominal S and A is obtained. Then these differences are added in quadrature to obtain a single uncertainty due to fixing these parameters.

• Signal and Background fraction: Signal fraction f sig is obtained using a two dimensional fit to M bc and ∆E, to study the impact of fixing it in the final four the fraction is varied by 10% and the difference between the obtained value of S and A and the initial one is taken as systematic uncertainty.

• Resolution function parametrization: The resolution function used in the analysis is modeled by three gaussians functions, when fitted on simulated data, some parameters are extracted and fixed in the final fit, thus to study this effect, these parameters by 1 sigma, then the uncertainties are summed in quadrature to obtain a single uncertainty.

• CP violation effect from BB background: The expected amount of BB events in the K* region (where M K 0 S π 0 ) is very small 6 % of total signal, where only neutral B (especially B 0 → X s0 γ ) can contribute to an uncertainty in S ∼ 0.008 this value was taken from previous experiments( Belle and Babar), and small contribution for C ∼ 0.002.

• Physics parameters: Parameters such as B 0 lifetime τ, and mixing parameter ∆m are fixed in the final fit in P sig (∆t), thus they are varied by an errors taken from the PDG (2016) and take the difference between the new values of S and A after shifting the two parameters, then sum them in quadratic.

• SVT alignment: The K 0 S momentum direction is determined from the information from the silicon vertex detector (SVD), thus mistakes in its alignment would affect the results, this source is mode independent. The uncertainties are taken from Belle analysis studies assuming having the same effect as in Belle II.

TDCVP Analysis of B 0 → K 0 S π + π -γ and B 0 → K 0 S π 0 γ Source ∆ S ∆A
B 0 → K 0 S π + π -γ
• Tag side interference: The interference between CKM-favored b → cud and doubly CKM suppressed b → uccd amplitudes in the tagging side B can effect time dependent CPV measurements. The uncertainties are taken from Belle that measures this effect by using the D * + L -ν decay.

All these sources are summarized and summed in quadraticure in table 4.5, where the highest uncertainty comes from fitting procedure source, which shows thate importance of modeling the PDFs using real data is cricial to minimize the effects of fixing these PDFs in the final fit. Also the systematics in the B 0 → K 0 S π + π -γ have been studied and summarized in the next section.

Systematics

B 0 → K 0 S π + π -γ
The same sources as above have been studied the same way for B 0 → K 0 S π + π -γ. tTable 4.6 summaries all the sources and the uncertainties and sum them in quadraticure assuming they are not correlated. The fitting procedure also has the highest uncertainty.

TDCVP Analysis of B 0 → K 0 S π + π -γ and B 0 → K 0 S π 0 γ S parameter S B 0 →K 0 S π 0 γ S B 0 →K 0 S π + π -γ
Belle II statistical uncertainty using 1 ab

Conclusion

As a conclusion to this analysis, a comparison with the statistical uncertainties reached by Belle is done. Table 5.14, reports the statistical uncertainties obtained in this analysis using Belle II simulated data of 1 ab -1 and the obtained uncertainties from latest Belle analysis for the same channels. The Belle II results are similar or slightly better than the Belle ones. This is an important finding, which demonstrates that the new Belle II vertex detector has the ability, in the simulation, to overcome the penalty of the lower boost available in SuperKEKB compared to the one prevailing at KEKB-Belle. The next chapter will explore the current status of vertexing in Belle II with a measure on real data. Regarding expectations for the full Belle II data set of 50 ab -1 , it appears that the measurement will still be statistically limited. Of course, this a preliminary investigation into the Belle II experiment performances. Already more advanced analysis tools are developed and they shall naturally increase the statistical power of TDCPV measurements.

CHAPTER 5

B 0 lifetime

Introduction

In this chapter, a new full analysis is presented, the B 0 lifetime measurement. As already revealed in Chapter 4, in TDCPV measurement, vertexing is the key to increase the sensitivity to time dependent analysis. To demonstrate the vertexing ability in Belle II, an analysis that measures the B 0 lifetime measurement, τ using the time difference measured between the two B 0 and B 0 pair will be a tool to cross-check the vertex fitting tools and time resolution modeling. This measurement is done using the early Phase3 dataset and fully reconstructed hadronic final states.

We follow a standard analysis procedure sharing similarities with the TD-CPV analysis according to the following overview. Similar to the TDCPV analysis, signal side B meson candidate is fully reconstructed but with hadronic decay final states. The rest-of-event technique allows to reconstruct the vertex position of the other B meson, still called tag side even if it is not used for tagging as the case in TDCPV analysis. The signal fraction estimation method is similar to the one used in TDCPV analysis, using a 2D fit to the M bc and ∆E distributions. Lifetime parameter τ is measured using a one dimensional fit to the time distribution. Each of the three time distributions, for signal, continuum and bb background are modeled. Nevertheless we developed a common functional for the time resolution model, adjusting the parameters specifically for each contributions. The functional form of the resolution model is set to be simple as it is B 0 lifetime measurement analysis the first modeling in starting Belle II analysis.

Datasets used

Simulations correspond to the Phase3 generic Υ(4S) MC13 sample, with 100 fb -1 . For real data, early Phase3 experiments of 2019 processing which amount to an integrated luminosity of about 10 fb -1 is used.

Event selection and reconstruction

Signal side

In this section, the reconstruction part of the analysis is presented in detail, starting from the final state particles reconstructed. Table 5.1 lists the hadronic final states, charge conjugate are implicitly assumed all along this chapter. Information on the vertex fit method and cuts specific to the channel are also provided. Whenever the TreeFitter is mentioned as the vertex fit tool, it is used without constraint from the interaction point and without constraining the mass of the intermediate particles.

Pions and kaons are identified as follows:

• The distance from the charged particle track to the interaction point in the rφ plane transverse to the beam is required to be less than 0.50 cm, and the track's z position from the interaction point is less than 3.0 cm. A selection based on particle identification likelihoods is used to identify π ± and K ± .

• Charged pions coming from the ρ ± or directly from the B d meson have an additional requirement: the momentum in the Υ(4S) center-of-mass frame of the mother particle must be larger than 0.20 GeV/c.

• π 0 candidates are formed from pairs of photons, with each photon having an energy greater than 30 MeV, 80 MeV, or 120 MeV if reconstructed in the barrel region, backward end-cap region, or forward end-cap region, respectively. The angle difference between the momenta of the two photons is required to be less than 0.90 radians and less than 1 radian for the angle in the rφ plane. The π 0 mass is required to be between 121 and 142 MeV/c 2 ; subsequently, a mass constrained fit is then performed and only candidates surviving the fit pass through the selection.

D 0 and D -reconstruction Three decay modes D 0 → K -π + ,D 0 → K -π + π 0 ,D 0 → K -π + π + π -are used to reconstruct D 0 , and D -→ K + π -π -is used to reconstruct D -. The standard deviation of the invariant mass distributions is ∼ 15 MeV/c 2 .

B 0 lifetime measurement analysis

Decay Selection Criteria B 0 decays B 0 → D -π + M bc > 5.2 GeV/c 2 and -0.2 < ∆E < 0.2 GeV B 0 → D -ρ + B 0 → D * -π + B 0 → D * -ρ + D decays D * + → D 0 π - 0.143 < m D * + -m D 0 < 0.147 GeV/c 2 D -→ K + π -π - |m -m PDG | < 0.015 GeV/c 2 D 0 → K -π + |m -m PDG | < 0.015 GeV/c 2 D 0 → K -π + π 0 D 0 → K -π + π + π - ρ decay ρ + → π + π 0 |m -m PDG | < 0.10 GeV/c 2

Tag side

In order to reconstruct the vertex of the second B 0 /B 0 in the event. An algorithm that uses all candidates left after reconstruction of the signal side, the vertex is reconstructed if two or more tracks are available with quality track cuts.

Signal and Tag side vertex fit

The fit to the signal and tag side vertices is performed as follows. The signal side vertex is reconstructed from the hadronic decays listed in Table 5.1 using a kinematic fit of the whole signal decay chain [START_REF] Krohn | Belle-II analysis software Group, Global Decay Chain Vertex Fitting at B-Factories[END_REF]. The tag side vertex position is determined from the tracks not used to reconstruct the signal side with an adaptive vertex fitter that accounts for the bias due to secondary decays [START_REF] Waltenberger | RAVE: A detector-independent toolkit to reconstruct vertices[END_REF].

Efficiencies

Efficiencies for reconstructing and selecting a given decay chain are evaluated with simulated data of 1 million signal events samples . The absolute efficiency is reported for each channel in table 5.2.

Decay

Selection efficiency %

B 0 → D -π + 51.5 ± 0.2 B 0 → D -ρ + 21.4 ± 0.2 B 0 → D * -π + 22.8 ± 0.2 B 0 → D * -ρ + 38.4 ± 0.22
Table 5.2: Selection efficiencies of studied processes, calculated using Phase 3 simulated data.

Continuum suppression

Rejection of the continuum events is done using two cuts, applied for all final states. Figure 5.2 shows the powering separation of these two variables, where R2 is the ratio between the 2-nd and 0-th Fox-Wolfram moments and cos θ thrust are defined and detailed in section 4.3.4.

• R 2 < 0.3,

• cos θ thrust (cosine of angle between thrust axis of the signal B 0 and thrust axis of rest of event ) < 0.8.

Time difference between the two B mesons

Recalling the definition of the proper time difference ∆t = t sigt tag between the two B meson candidates (signal and tag) is approximated from the distance ∆z boost between the two reconstructed vertices along the collision boost direction β as follows;

∆t = ∆z boost βγ c . ( 5.1)
The Υ(4S) boost in the center of mass momentum yields an event-independent value of γβ Υ = 0.28.

For each event, the uncertainty σ ∆t on the calculated ∆t is computed. Candidates are required to pass two additional cuts,where the cut on σ ∆t can be verified in Figure 5.4.

• |∆t| < 8 ps,

• σ ∆t < 3.5 ps.

Fit to get signal and background fractions

In order to fit the time distribution model ∆t, unbinned likelihood performed and defined later in equation 5.8, this PDF requires the number of events for each population in the data sample. Three different populations contribute to the selected sample: signal, bb background and continuum background. The contribution from each population is thus estimated from a 2D unbinned maximum likelihood fit of the B-meson constrained mass M bc and ∆E distribution, this 2D fit has been developed by the Belle II-France member Giulio Dujany. In section 5.4.1, the probability distribution functions used to describe the three populations are presented, these PDFs are chosen using simulated samples containing only one population. Projections of the 2-D fit to each population is shown in Figures 5.5, 5.6 and 5.7 for all decay channels together, as well, their corresponding tables listing the parameters extracted from the fit. In section 5.4.2, the fit to extract the signal and background yields is presented, using simulated data and real data, plus a comparison between the yields obtained is shown.

The fits are performed over all decay channels used in this analysis considered without using a different distribution for each different decay channel. To check against possible biases, fits are also performed separately for each decay channel (see Table 5.3) and the sum of the yields coming from the different channels are compared with the yields from the common fit and found to be compatible. The fit projections for the fit on simulated data to the individual decay channels can be found in Appendix 5.8. In the separate fits, due to the smaller sample size and the different shapes simpler distributions are often used as detailed in the sections.

Channel number

Decay channel

2 B d → D -ρ + 3 B d → D -π + 7 B d → D * -ρ + (D 0 → K -π + ) 8 B d → D * -ρ + (D 0 → K -π + π 0 ) 10 B d → D * -π + (D 0 → K -π + ) 11 B d → D * -π + (D 0 → K -π + π 0 )

Population distirbutions for M bc and ∆E

Signal distribution for M bc and ∆E

The signal is described by a Johnson's S U distribution for both M bc and ∆E distributions parameterized as

J (x; µ, σ, γ, δ) ∝ e -1 2 (γ+δ sinh -1 (z)) 2 √ 1 + z 2 with z = x -µ σ Figure 5
.5 shows the projections in M bc and ∆E of the fit of all the channels together while the plots of the separate components can be found in section .4. The fit parameters are collected in Tables 5. [START_REF] Ushiroda | Belle, Time-Dependent CP Asymmetries in B 0 → K 0 S π 0 γ transitions[END_REF]. B 0 lifetime measurement analysis To better describe the correlation between M bc and ∆E of the bb population, its distribution is separated in two components: one with a peaking shape and other one with a a continuum shape. That two components are then summed together (the parameter f denotes the relative normalization of the peeking component) as:

M bc ∆E Channel µ [GeV/c 2 ] σ [GeV/c 2 ] γ δ µ [GeV] σ [GeV] γ δ 2 5.
P bb = f P bb, peak + (1 -f )P bb, cont
P bb, peak is described by a Johnson's S U distribution in M bc and by the sum of three Gaussian distributions in ∆E, parameterized as

f 1 • G(∆E; µ, σ) + f 2 • G(∆E; µ + dµ, s • σ) + (1 -f 1 -f 2 ) • G(∆E; µ + dµ ′ , s ′ • σ)
Where G(x; µ, σ) denotes a Gaussian distribution with mean µ and width σ.

P bb, cont is described by an Argus distribution in M bc as:

Argus(x) ∝ t • 1 -t 2 • exp[-χ(1 -t 2 )] with t = x x 0 .
with x 0 = 5.29 GeV/c 2 . The continuum shape is described by an exponential distribution in ∆E: exp (α • ∆E).

In the separate fits only one or two Gaussian is used to describe the ∆E peeking component. Moreover for B d → D -ρ + the correlation between M bc and ∆E is neglected and peeking and continuum components are added separately for M bc and ∆E with different fractions ( f for M bc and f ′ for ∆E). Figure 5.6 shows the projections in M bc and ∆E of the fit of all the channels together while the plots of the separate components can be found in Appendix .4. The fit parameters are collected in Tables 5. [START_REF] Li | Belle, Time-dependent CP Asymmetries in B 0 → K 0 S rho 0 γ Decays[END_REF].

Continuum background distribution for M bc and ∆E

The continuum background is described by an Argus distribution for M bc and an exponential distribution for ∆E. B 0 lifetime measurement analysis of the fit of all the channels together while the plots of the separate components can be found in Appendix .4. The fit parameters are collected in Table 5.6.

Peaking Continuum M bc ∆E M bc ∆E Channel µ [GeV/c 2 ] σ [GeV/c 2 ] γ δ µ [GeV] σ [GeV] χ α [GeV -1 ] f 2 5.
M bc ∆E Channel χ α [GeV -1 ] 2 -23.8 ± 1.6 -1.73 ± 0.14 3 -20.1 ± 1.6 -1.84 ± 0.14 7 -17 ± 6 -1.0 ± 0.5 8 -1 ± 6 -1.2 ± 0.

Fit to M bc and ∆E to extract the signal and background contributions

In the fit to extract the yields of the three different populations the distributions for the three components are fixed to the ones described in the previous sections. All the parameters are fixed except for the three yields and the mean and the width of a Gaussian of the signal population to account for the possible data-MC difference. The mean of the other peaking components are also shifted by fixing their differences with respect to the mean left floating to the values from simulation. The scaling value between the width of the peeking components and the width left floating is also fixed from simulation. Figure 5.8 shows the projections in M bc and ∆E of the fit on MC while Figure 5.9 shows the projections of the fit on data. The fit projections for the fit on MC to the individual decay channels can be found in Appendix .4. Table 5.7 collects the fit parameters. Table 5.8 compares the yields of the three components obtained from the fit B 0 lifetime measurement analysis to the true ones from simulation. Table 5.9 contains the same information but for the signal region (5.25 < M bc < 5.29 GeV/c 2 and -0.07 < ∆E < 0.05 GeV) that is shown in Figure 5.11. A satisfactory agreement between fit and true value is obtained in every decay channel and also combining all the decay channels together (Figure 5.10). Moreover there is a good agreement between the yields obtained from the common fit and the sum of the yields of the individual fits. 5.9: Fit yields in signal region. The row Sum contains the sum of the yields of the individual modes, the raw All contains the yields considering together all the modes while the raw Data contains the result of the fit to the data. The columns pull i are defined as

B
(n i -n true i )/σ n i .

Signal ∆t distribution Models P sgn

The signal distribution, P sgn , is modeled by the convolution between the distribution describing an exponential decay, P th (5.4), and the resolution function R described in (5.9) as shown in equation (5.5).

P th (∆t) = 1 2τ B exp - |∆t| τ B . (5.4)
P sig (∆t) = +∞ -∞ P th (∆t ′ )R(∆t -∆t ′ )d∆t ′ . ( 5.5)
To check potential bias in the reconstruction, the profile distribution of the residual on ∆z (distance along z between the signal and tag vertex in the event) versus the true ∆z for true reconstructed signal candidates is shown in bias can be understood considering separately the z vertex residuals for the signal and tag vertices. bb background ∆t distribution P bb Unlike in the continuum background case, the ∆t distribution of the bb background events cannot be simply described by a sum of Gaussian distributions because, like in the signal case, the lifetime of the decaying B mesons cannot be neglected. Like in for the signal case the correct description will thus be the convolution of an exponential decay function with the resolution function as described in (5.6).

P bb (∆t) = +∞ -∞ 1 2τ e f f exp - |∆t ′ | τ e f f R(∆t -∆t ′ )d∆t ′ . (5.6)
The resolution function is exactly the same as the one used for the signal while instead of the B 0 lifetime an effective lifetime τ e f f is used. Figure 5.17 shows the fit to the ∆t distribution of bb events in the ∆E-M bc signal range. The distribution in (5.6) is used. The parameters of the resolution function are fixed to the ones obtained from the signal fit shown in fig 5 .15 and only the effective lifetime is left free. The fitted τ e f f value is 1.39 ± 0.064 ps and it will be fixed in the final fit. The superimposed fit follows the pdf defined in (5.6).

Full fit ∆t distribution P all

The B 0 lifetime is extracted with an unbinned maximum likelihood fit to the ∆t distribution using (5.8) as model. The yields of the three populations are fixed to the ones obtained in Section 5.4. All the parameters of P cont are fixed as explained in Section 5.5.1. P sgn and P bb share the same resolution function whose parameters are all fixed to the ones obtained in Section 5.5.1 except for µ 1 and σ 1 (see Table 5.11). Figure 5.18 shows the result of this fit on the simulated sample. The obtained value of the B lifetime is compatible with the generated one. Parameter Value used P all µ 1 cont -0.007 fixed from MC sideband fit, Figure 5.12 (right) σ 1 cont 0.401 fixed from MC sideband fit, Figure 5.12 (right) dm cont -0.0846 fixed from MC sideband fit, Figure 5.12 (right) f 1 cont 0.468 fixed from MC sideband fit, Figure 5.12 (right) f 2 cont 0.357 fixed from MC sideband fit, Figure 5.12 (right) s2 cont 2.88 fixed from MC sideband fit, Figure 5.12 (right) s3 cont 3.02 fixed from MC sideband fit, Figure 5.12 (right) Table 5.11: Parameters used the final fit on MC in Figure 5.18, P cont parameters are all fixed from the fit to the sideband events, P sgn and P bb share the same resolution where only µ 1 and σ 1 are floating.

Coutntinuum background ∆t distribution from data sideband

As described in Section 5.5.1 the shape of the Continuum background ∆t distribution in the final fit to extract the B 0 lifetime will be completely fixed. Its yield is fixed from the M bc -∆E fit of Section 5.4 while its shape is determined from a fit to a sideband in M bc , ∆E, R 2 and cos θ thrust . Figure 5.19 shows the result of this fit. The distribution is fitted with the sum of three Gaussian distributions with all the parameters fixed to the values obtained from the fit to the simulated candidates except a common mean and sigma to allow for data-MC differences.

The parameters obtained from the fit to the data are compatible with the values from the fit to simulated candidates.

Unblinding

The unblinding with the whole sample of data as been performed. Its result can be seen in Figure 5.20 and Table 5.12. The measured lifetime is τ = 1.48 ± 0.28 which is compatible with the known value. 271 fixed from 2D fit on data, Figure 5.9 n cont 142 fixed from 2D fit on data, Figure 5.9

Table 5.12: Parameters used the final fit for data in Figure 5.20, P cont parameters are all fixed from the fit to the sideband events, P sgn and P bb share the same resolution where only µ 1 and σ 1 are floating.

Systematic uncertainties and cross checks

The statistical uncertainty associated to this measurement is about 20% while the B 0 lifetime is known with a 0.3% uncertainty. Consequently, systematic studies only focused on the two main expected uncertainty sources: the parameterization of each time distribution contribution (partly fixed from simulated data) and the vertices reconstruction (embedding potential alignment and calibration effects).

Fit systematic uncertainty

Ten thousand toy datasets with a statistic equivalent to the one of the data sample have been obtained via the bootstrapping technique from a 100 fb -1 MC13 sample independent from the one used to develop the analysis. For each one of the samples we performed the strategy used on data: M bc -∆E fit, fit to the sideband to extract the shape of the continuum component and final fit to extract the B 0 lifetime. Figure 5.21 shows the difference with respect the true value of value of τ obtained with the procedure used on data obtained with a toy study and the corresponding pull distribution. A 3% bias is observed (-0.05 ps is the mean of the distribution of differences, blue bashed line in the figure). We assign as systematic uncertainty due to the fit procedure 0.05 ps. The central range containing 68.3% of the toys that corresponds to the fraction contained within 1 σ in a Gaussian distribution (red dashed-dotted lines in the figure) has an half-width of 0.28 ps, the same value obtained as statistical error by the fit.

Systematic uncertainty for fixing τ e f f from simulation

The previous systematic uncertainty accounts for the bias in the fit strategy. It cannot however take into account the fit bias due data-MC differences as it is based on simulated samples. To take into account the data-MC difference some parameters of the resolution function and of the distribution for continuum events are obtained fitting the data. It is not possible however to determine the value of τ e f f in a data driven way. The B 0 lifetime fit is thus repeated leaving also τ e f f free (Figure 5.22). The difference with the lifetime obtained in the baseline fit is taken as systematic uncertainty. This amounts to 0.01 ps, which corresponds to a 0.7% relative systematic uncertainty.

Calibration and alignment systematic uncertainty

Another cross-check that can provide information on the systematic uncertainty due to the calibration and alignment quality is to extract the B 0 lifetime separately on three samples called in Belle II software as, proc9+bucket7, proc10 and bucket8 where proc10 corresponds to the same dataset as proc9+bucket7 but reconstructed with a better calibration and alignment. 5.13 contain the result of the same fit strategy used on data but applied on the different data samples. The fitted lifetime is compatible between the three samples which indicates that the possible systematic uncertainty is negligible with respect to the statistical uncertainty. A more precise estimate of the uncertainty linked to the calibration and alignment quality can be obtained by comparing the values from proc9+bucket7 and proc10 that correspond to the same dataset but with a different alignment and calibration. The difference of 0.03 ps would corresponds to a systematic uncertainty of 2%. We assign as systematic uncertainty due to the calibration and alignment 0.03 ps.

Total systematic uncertainty

The overall systematic uncertainty is obtained as a quadratic sum of the three contributions described above and amount to 0.06 ps or 4% relative uncertainty.

Conclusion

A first measurement of the B d lifetime was performed with the 2019 Belle II data set, which amounts to an integrated luminosity of 8.7 ± 0.2 fb -1 . The estimated lifetime is τ B d = 1.48 ± 0.28 ± 0.06 ps, where the first uncertainty is statistical and the second is systematic. This value is compatible with the world average of 1.519 ± 0.004 ps [START_REF] Tanabashi | Review of Particle Physics[END_REF]. This analysis is a first step showing that the Belle II vertex detector delivers the expected performances and was publicly communicated outside Belle II [START_REF] Abudinén | Belle-II, Measurement of the B 0 lifetime using fully reconstructed hadronic decays in the 2019 Belle II dataset[END_REF]. Indeed, the resolution on the distance between the two B mesons is found o be 80 µm, approaching the expected 60 µm.

Conclusion

A first implementation of the measurement of the Time dependent CP violation parameters in radiative B 0 decays is done using Belle II simulated data. The technique is then applied to the simulated data equivalent to 1 ab -1 integrated luminosity collected at the Υ(4S) resonance from the SuperKEKB asymmetric e + ecollider. Two radiative decay channels are investigated B 0 → K 0 S π + π -γ and B 0 → K 0 S π 0 γ, to yield the following results:

S B 0 →K 0 S π + π -γ = -0.09 ± 0.2 ± 0.026 S B 0 →K 0 S π 0 γ = 0.02 ± 0.3 ± 0.02 A B 0 →K 0 S π + π -γ = -0.21 ± 0.17 ± 0.025 A B 0 →K 0 S π 0 γ = 0.03 ± 0.19 ± 0.024
where the first uncertainty is statistical and the second is systematic. Our measurement results is compatible in precision with the Belle and Babar published results and using about the same integrated luminosity. A toy Monte Carlo study have been done using 200 toy experiments to extract the prospects of the statistical uncertainty with more data, as the Belle II program targets an integrated luminosity corresponding to 50 ab -1 . Figure 5.25 shows the calculated statistical uncertainty of the measured CP violation parameters S and A as function of the integrated luminosity for the B 0 → K 0 S π 0 γ channel, the Belle and Babar statistical level is superimposed. Figure 5.26 similarly shows the statistical uncertainty for B 0 → K 0 S π + π -γ using also 200 toy Monte Carlo experiments. The figure reveals a promising result with the full Belle II dataset, where the expected statistical uncertainties for Belle II reach levels below the systematic one from Belle ∼ 0.05. However, such uncertainties cannot be directly converted into discovery potential for New Physics, since non CP eigenstates in this channel can dilute the precision on S. The next step regarding Time dependent CP violation in radiative B 0 decays will be the rediscovery of the two decay channels in the coming year (2021) with an integrated luminosity expecting to exceed 100 fb -1 .

Conclusion

As a complementary work to the TDCPV analysis and since data accumulated in 2019 was still not enough to run this analysis on real data. A demonstration of the vertexing performances has been studied, due its central importance for time-dependent analysis. A first measurement of the B 0 lifetime using hadronic decays is done on real data accumulated 2019 Belle II data set, which amounts to an integrated luminosity of 8.7 ± 0.2 fb -1 . The result of this mea- surement is:

τ B d = 1.48 ± 0.28 ± 0.06 ps
where the first uncertainty is statistical and the second is systematical. This value is compatible with the world average of 1.519 ± 0.004 ps [START_REF] Tanabashi | Review of Particle Physics[END_REF]. Although the statistical uncertainty is quite large, the much smaller systematics demonstrates Belle II readiness for measurements with its vertex detector. One should note in addition, that this analysis uses a rather simple time resolution model to account for detector effects on the evaluation of decay time difference ∆t beteen the two B mesons in the event. This strategy was chosen to reach a finalized measurement in a timely manner. Clearly more studies on ∆t measurement and resolution parametrisation are needed and will benefit the statistical power of time dependent analysis. For example, a constraint on the vertex fit to the interaction point, which is very well known owing to the smallness of the beam size, bias the lifetime parameter measurement, since it shifts the ∆z distribution. Already with the accumulated luminosity reached currently, a more complex resolution model reproducing the various reconstruction effects is needed and can be developped.

RÉSUMÉ français

→ K 0 s π + π -γ et B 0 → K 0 s π 0 γ.
Les rapports d'embranch A first measurement of the B d lifetime was performed with the 2019 Belle II data set, which amounts to an integrated luminosity of 8.7 ± 0.2 fb -1 . The estimated lifetime is τ B d = 1.48 ± 0.28 ± 0.06 ps, where the first uncertainty is statistical and the second is systematic. This value is compatible with the world average of 1.519 ± 0.004 ps [START_REF] Tanabashi | Review of Particle Physics[END_REF]. This analysis is a first step showing that the Belle II vertex detector delivers the expected performances and was publicly communicated outside Belle II [START_REF] Abudinén | Belle-II, Measurement of the B 0 lifetime using fully reconstructed hadronic decays in the 2019 Belle II dataset[END_REF]. Indeed, the resolution on the distance between the two B mesons is found o be 80 µm, approaching the expected 60 µm.ement de ces canaux sont relativement petits, respectivement de 7 × 10 -6 et 9.5 × 10 -6 . Les mesures existantes sur ces canaux ont été effectuées par les expériences Belle [4] [START_REF] Li | Belle, Time-dependent CP Asymmetries in B 0 → K 0 S rho 0 γ Decays[END_REF] et Babar [START_REF] Aubert | Measurement of Time-Dependent CP Asymmetry in B 0 → K 0 S π 0 γ Decays[END_REF] [7] à partir d'une luminostié intégrée légèrement inférieure à 1 ab -1 et n'ont pas donné de résultats statistiquement significatifs pour la recherche de nouvelles physiques. Mon objectif était d'étudier la sensibilité de ces canaux pour obtenir une valeur non nulle de le paramètre S de violation indirecte du CP en utilisant TDCPV analyse avec l'ensemble de données Belle II. Je commence à travailler avec des données issues de la simulation complète du détecteur pour paramétrer et affiner l'analyse des désintégrations radiatives des mésons B, qui consiste à sélectionner des événements potentiellement correspondant à notre canal puis effectuer un ajustement à quatre dimensions des données afin d'extraire le paramètres de violation de CP, S et C. Pour finaliser l'analyse, j'ai évalué les incertitudes systématiques possibles de plusieurs sources pour les deux canaux. Ensuite, j'ai développé la première mesure de la durée de vie de B 0 avec des données réelles dans Belle II, la durée de vie de B 0 est précisément mesurée dans des expériences de physique des particules, la mesurer dans Belle II est une première démonstration des outils utilisés pour l'analyse TDCPV. La mesure de la durée de vie de B 0 a été documentée dans un article de la conférence Belle II, rapporté dans les conférences d'hiver 2020 et publié en mai 2020. La mise en service de l'accélérateur SuperKEKB a été réalisée, en phase 1, les anneaux d'accélération ont été mis en service sans le système de focalisation finale au point d'interaction sans le détecteur Belle II. Au cours de la phase 2, la mise au point finale et l'anneau amortisseur de positrons sont en place, ainsi que le détecteur Belle II, à l'exception du détecteur de vertex où, à la place, le détecteur BEAST a été installé pour mettre en service la machine en mesurant les taux de fond du faisceau et assurer la sécurité radiologique de Belle II pour fonctionner à une luminosité plus élevée. Dans la phase 3, le détecteur de vertex complet a été installé et a commencé à prendre des données en mars 2019, le plan est d'atteindre une luminosité élevée de 50 ab -1 , permettra d'avoir un ensemble de données pour avoir une précision sur l'analyse TDCPV.

Sensibilité de l'analyse TDCPV

Dans cette section, les principaux principes utilisés pour effectuer l'analyse CP en fonction du temps sont énumérés. Belle II fournit des collisions électronpositon, à une résonance de 10.58 GeV se désintègre en une paire de BB et cette paire est au repos dans le Υ(4S) centre de masse système. Cette paire est produite dans un état cohérent quantique, ce qui signifie que lorsque le méson B subit un mélange de saveurs et un méson change de saveur, l'autre change automatiquement de saveur aussi. Ce fait permet la technique dite "flavour tagging". Dans cette analyse, nous notons B 0 tag qui est identifié expérimentalement par reconstruction inclusive et par entaglement quantique, l'autre saveur B 0 sig est connue à t tag . Ensuite, comme B 0 sig se décompose en deux désintégrations radiatives, la différence de temps ∆t peut être mesurée à partir de ∆z, la distance entre les sommets de désintégration de B 0 tag et B 0 sig . Enfin, les paramètres TDCPV sont extraits de la distribution ∆t.

Marquage des saveurs est nécessaire à l'analyse TDCPV, la tâche est de déterminer le flavor de B 0 tag au moment de son disintegration. B 0 mesons fourni des signatures de saveurs par des états finaux saveurs spécifiques. Après avoir connu la saveur des deux mésons B 0 , et afin d'obtenir des S et A corrects, les effets expérimentaux doivent être pris et la fonction de densité de probabilité obtenue à partir des taux de décroissance est utilisée pour ajuster la distribution temporelle comme suit: Mon travail dans l'analyse TDCPV s'est principalement porté sur la première (sélection) et la dernière étape (systématique), les autres étant prises en charge par un post-doctorant du groupe.

P (∆t, q) = f sig e -|∆t|/τ B 0 4τ B 0 [1 -q∆w + (1 -2w)qA cos(∆M∆t)+ S sin(∆M∆t)] ⊗ R sig (∆t) -(1 -f sig )P bkg (∆t) (5

Optimisation de la sélection :

Avec le détecteur Belle II, nous mesurons l'ensemble des caractéristiques des (N S : candidats de signal, N B : candidats de bruit de fond) [START_REF] Del Amo | BaBar, Time-dependent analysis of B 0 → K 0 S ππ + γ decays and studies of the K + ππ + system in B + → K + ππ + γ decays[END_REF]. Après avoir fait l'optimisation complète, j'ai atteint une signifiance maximale de ∼ 6. Figure 5.31 indique la première étape utilisée pour obtenir une signification maximale. Méthode de l'extraction la durée de vie B 0 Pour mesurer la durée de vie B 0 des candidats sélectionnés, un ajustement de probabilité non binné est effectué sur la distribution globale ∆t. La distribution des probabilités dans l'équation (5.8) décrit cette distribution globale en combinant les rendements de contribution mesurés dans la section 5.4. P all (∆t) = n sgn P sgn (∆t) + n bb P bb (∆t) + n cont P cont (∆t).

Systematics study:

(5.8)

Les modèles analytiques de distribution de ∆t pour les trois principales contributions à l'échantillon candidat sont décrits dans la section 5.5.1.

Un élément important de l'ajustement pour extraire la durée de vie B est la résolution fonction R qui décrit le frottement introduit par divers effets au cours de la reconstruction. Dans cette analyse, R est modélisé par la somme de trois distributions gaussiennes(5.9).

R(δ

∆t ) = f 1 G(δ ∆t ; µ 1 , σ 1 ) + f 2 G(δ ∆t ; µ 1 + dm, s 2 × σ 1 ) +(1 -f 1 -f 2 )G(δ ∆t ; µ 1 , s 2 × s 3 × σ 1 )
(5.9)

Une fonction de résolution universelle est utilisée et non fonction candidat par candidat fonction, en fonction par exemple de l'incertitude sur ∆t due à la petite taille de l'échantillon considéré dans cette analyse.Cette résolution est également utilisée pour ajuster la fonction ∆z des deux côtés, signal et tag. 8.7 ± 0.2 fb -1 . La durée de vie estimée est τ B d = 1.48 ± 0.28 ± 0.06 ps, où la première incertitude est statistique et la seconde est systématique. Cette valeur est compatible avec la moyenne mondiale de 1.519 ± 0.004 ps [START_REF] Tanabashi | Review of Particle Physics[END_REF].

Cette analyse est une première étape montrant que le vertex détecteur de Belle II fournit les performances attendues et a été publiquement communiqué en dehors de Belle II [START_REF] Abudinén | Belle-II, Measurement of the B 0 lifetime using fully reconstructed hadronic decays in the 2019 Belle II dataset[END_REF]. En effet, la résolution sur la distance entre les deux mésons B se trouve être de 80 µm, approchant les 60 µm attendus.

Conclusion

La mesure de la violation de la symétrie CP est l'un des programmes principaux et prometteurs du projet Belle II visant à découvrir la nouvelle physique. Durant ma thèse, j'ai quantifié avec des données simulées la précision atteignable avec une analyse TDCVP des désintégrations radiatives des mésons B 0 . Cette analyse donne les résultats suivants : xiii S B 0 →K 0 S π + π -γ = -0.09 ± 0.2 ± 0.026 S B 0 →K 0 S π 0 γ = 0.02 ± 0.3 ± 0.02 A B 0 →K 0 S π + π -γ = -0.21 ± 0.17 ± 0.025 A B 0 →K 0 S π 0 γ = 0.03 ± 0.19 ± 0.024 la première incertitude est statistique et la seconde est systématique. Nos résultats de mesure sont compatibles en termes de précision avec les résultats publiés par Belle et Babar et utilisent la même luminosité intégrée. La prochaine étape concernant la violation du Time dependent CP dans les décroissances radiatives B 0 sera la redécouverte des deux canaux dans l'année à venir (2021) avec une luminosité intégrée qui devrait dépasser 100 fb -1 . Par ailleurs, étant donné que les données de Belle II accumulées en 2019 n'étaient pas suffisantes pour démarrer cette analyse TDCVP, j'ai développé une autre analyse complète en utilisant les désintégrations du méson hadronique B pour mesurer la durée de vie pour la première fois dans Belle II. Cette mesure est un premier pas nécessaire pour mettre en place des mesures de type TDCPV.

Une première mesure de la durée de vie de B 0 utilisant des désintégrations hadroniques est effectuée sur des données réelles accumulées 2019 Belle II, équivaut à une luminosité intégrée de 8, 7 ± 0, 2 fb -1 . Le résultat est : τ B d = 1.48 ± 0.28 ± 0.06 ps la première incertitude est statistique et la seconde est systématique. Cette valeur est compatible avec la moyenne mondiale de 1.519 ± 0.004 ps [START_REF] Tanabashi | Review of Particle Physics[END_REF]. Bien que l'incertitude statistique soit assez grande, la systématique beaucoup plus petite démontre que Belle II est prête pour des mesures avec son détecteur de vertex.

xiv

Probability density functions

In this section, I give the definitions of the PDFs used in the fits

.1 Gaussian function

The expression for the standard Gaussian function is defined as:

G(x, µ, σ) = 1 a exp 1 2 x -µ σ 2
The parameters µ and σ are the mean and the width of the Gaussian; 1 a is a normalization constant.

.

Crystal Ball function

The expression for the standard Crystal Ball function is given as:

CB(x, µ, σ, α, ) ∝        ( n α ) n exp(-α 2 /2) ((µ-x)/σ+n/α-α) n x ≤ µ -ασ exp 1 2 ( x-µ σ ) 2 x > µ -ασ       
The parameters µ and σ describes a Gaussian, which is truncated on the low side at µασ and joined continuously to a power function with an exponent n, 1 a is a normalization constant.

.3 Argus function

The Argus function is given by: Argus(x, x 0 , χ) = 1

a t • 1 -t 2 • exp[-χ(1 -t 2 )] with t = x x 0 .

Probability density functions

The parameter χ is the Argus shape parameter, the cutoff x 0 is the nominal beam energy, and 1 a normalization constant.

. Two dimensional fits get signal and background fractions for channels

Chebychev function

Figure 1 . 1 :

 11 Figure 1.1: The elementary particles of the standard model. For each particle, mass, charge, spin and name are given. They are divided into three generations of quarks and leptons, gauge bosons as force carriers, and the Higgs boson. The fermions are shown in the same order as in the weak isospin doublets.

  with L a the Gell-Mann matrices and σ b the Pauli matrices. G µ a , W µ b and B µ are the eight gluon fields, the three weak interaction bosons and the single hypercharge boson, respectively.

Figure 1 . 2

 12 Figure 1.2

Figure 1 . 3 :

 13 Figure 1.3: Experimental constraints of the unitarity traingle in ρη plane, results of the most updated extrapolations from the CKM Fitter group (ICHEP 2018 conference) are shown [18].

Figure 2 . 1 :

 21 Figure 2.1: Diagrams describing the mixing phenomenon for neutral B d mesons via a second order weak transition, usually called box diagrams.

Figure 2 . 2 :

 22 Figure 2.2: Feynman diagrams for the amplitudes contributing to the B 0 → J/ψK 0 S decay. Left: Tree level diagram. Right: Penguin diagram, where the contribution of the light, u and c, quarks have been neglected. The dotted line corresponds to the exchange of three gluons, necessary to produce a cc pair.

  Figure 2.3 candidates for such particles are for instance charged Higgs or squarks

Figure 2 . 3 :

 23 Figure 2.3: Diagrams demonstrating the potential for new physics sensitivity in b → s penguin diagrams.

Figure 2 . 4 :

 24 Figure 2.4: Feynman diagram of b → s γ transition in the SM. The loop being dominated by the top quark, the weak couplings are given by |V * qb | ∼ 1 and |V qs | ∼ λ 2 . In this transition since the b → sγ transition is a two-body back-to-back decay in the b rest frame, and due to the helicity conservation, the photon must be right-handed, while being left-handed in b → sγ.

Figure 2 .

 2 4 shows the Feynman diagram of the quark level b → sγ transition in the SM.

Figure 3 . 1 :

 31 Figure 3.1: A schematic representation of the SuperKEKB asymmetric energy e + e -collider

Figure 3 . 2 :

 32 Figure 3.2: Fundamental parameters at KEKB and at SuperKEKB

Figure 3 . 3 :

 33 Figure 3.3: Schematic view of the beam crossing at KEKB (top) and at SuperKEKB (bottom). The crossing angle is shown in the top. The beam directions are shown in the bottom scheme. The size of the interaction region in z-direction at KEKB was around 10 mm, while at SuperKEKB it is around 0.5 mm

Figure 3 . 4 :

 34 Figure 3.4: The integrated luminosity collected during the Phase 2 run, April-July 2018, is shown. The various curves refer to the trigger information available for each data set

Figure 3 . 5 :

 35 Figure 3.5: The CAD rendering and a real image of the vertex detector cartridge and BEAST II monitoring setup installed during Phase 2 at the interaction point.

Figure 3 . 6 :

 36 Figure 3.6: Illustration showing in the top, the upgraded Belle II detector as designed in the Belle II Technical design report[START_REF] Abe | Belle-II[END_REF], while in the bottom, the longitudinal view of the old Belle detector is shown.

Figure 3 . 7 :

 37 Figure 3.7: A shematic view of the Belle II vertex detector, two pixelated layers and four layers with silicon strip sensors

Figure 3 . 8 :

 38 Figure 3.8: Layer configuration of the CDC at Belle (top) and at Belle II (bottom). The letter A stays for axial superlayers; the letter U for stereo superlayers with positive stereo angle; and the letter V for stereo superlayers with negative stereo angle.

Figure 3 . 9 :

 39 Figure 3.9: Left: Schematic view of the SVD longitudinal section, showing the sensors geometry for each layer and the number of APV25 chips on each side of the sensors. Right: the windmill structure of the inner sensors, with the Origami concept applied on the upper edge of silicon modules, is shown.

Figure 3 . 10 :Figure 3 . 11 :

 310311 Figure 3.10: Conceptual overview of TOP counter

Figure 3 . 12 :

 312 Figure 3.12: Schematic side-view of TOP counter and internal reflecting Cherenkov photons.

Figure 3 . 13 :

 313 Figure 3.13: Proximity focusing ARICH -principle

Figure 3 . 14 :

 314 Figure 3.14: Kaon efficiency and pion mis-ID rate for the PID criterion R K/π > 0.5 using the decay D * + → D 0 [K -π + ]π + in the bins of laboratory frame momentum of the tracks.

Figure 3 . 15 :

 315 Figure 3.15: Kaon efficiency and pion mis-ID rate for the PID criterion R K/π > 0.5 using the decay D * + → D 0 [K -π + ]π + in the bins of polar angle (laboratory frame) of the tracks.

Figure 3 . 16 :

 316 Figure 3.16: Schematic overview of the data flow from the detector readout followed by the different trigger stages up to storage devices. The stored data is then processed and used for physics analysis. The shown data rates are preliminary and are taken from the current software simulation using the physics rates in [].

Figure 4 . 1 :

 41 Figure 4.1: B rec denotes the reconstructed decaying into states of interest. Evaluation of the CP violating asymmetries requires knowing the flavour of the B 0 meson at its decay time. This is achieved by identifying the decay channel of the other B 0 meson, B 0 tag , inclusively reconstructed, the knowledge of the difference between the decay times of both B mesons allows us to infer the flavour of B 0 sig . The time elapsed between the two decays can be calculated from the distance ∆z measured between the two B decay vertices along the beam direction z.

Figure 4 . 2 :

 42 Figure 4.2: Schematic overview of the Flavour Tagger: Reconstructed tracks are available for five different mass hypotheses. Each green box corresponds to a category.The event-level process is performed within each individual category. Then to each particle candidate a probability y cand is assigned, then combined to provide the final q.r output.

  Figure 4.4, I show one of the newest studies, the comparison of efficiencies obtained with the Belle II flavor tagger for 2019 Belle II data and with the Belle flavor tagger in Belle data. The performance of the Belle II flavor tagger is comparable with the best one obtained by the Belle experiment, thanks to the new Belle II category-based flavor tagger considering more flavor signatures and more input variables.

Figure 4 . 3 :

 43 Figure 4.3: Results of the Flavor tagger FBDT combiner using a) Belle II MC and b) Belle MC. Left: Distribution of the q.r output. Right: Truth matched dilution r MC = 1 -2w MC taken from MC truth in each r-bin. The errors on both axes are not visible due to their small size. The red diagonal line is a guideline and the vertical grey lines correspond to the limits of the r-bins.

Figure 4 . 4 :

 44 Figure 4.4: Performance of the Belle II flavor tagger in 2019 Belle II data and of the Belle flavor taggerin Belle data[START_REF] Bevan | The Physics of the B Factories[END_REF] taken with the second silicon-vertex detector configuration(SVD2)

Figure 4 . 5 :

 45 Figure 4.5: Distributions of ∆t (left) for B 0 → K 0 S π + π -γ, and σ ∆t (right) for signal MC events (blue), data challenge (black dots), full simulated data sample (Gray).

Figure 4 . 6 :

 46 Figure 4.6: Distributions of the two kinematical variables fof B 0 → K 0 S π + π -γ, M bc (left) and ∆E (right) for signal MC events (blue), full simulated data (black), full MC sample (Gray).

Figure 4 . 7 :

 47 Figure 4.7: Decay products of B mesons are distributed isotropically, forming the event with spherical geometry. Particles from continuum events form the jet-like geometry of an event

√S 2 •

 2 S+B is measured as function of the variable cut values, as shown in Figure 5.31. • The variable reaching the highest significance, d K 0 All cuts are applied and again the S √ S+B of the variable chosen, d K 0 S /σ(d K 0 S ) is varied to obtain a larger maximum significance, this step showed for d K 0 S /σ(d K 0 S ) > 9, S √ S+B = 20 is reached. • In the third step, the cut d K 0 S /σ(d K 0 S

Figure 4 . 8 :

 48 Figure 4.8: The S √ S+B distributions as function of the cuts variables range

Figure 4 . 9 :

 49 Figure 4.9: Projection of the four dimensional fit to each of M bc , ∆E, ∆t, CSMVA for B 0 → K 0 S π 0 γ. The fit is done using simulated data of 1 ab -1 . The combined probability distribution function is represented by the solid blue line while the two components are represented by a dotted green for BB background and dotted gray for continuum background.

Figure 4 . 10 :

 410 Figure 4.10: Projection of the four dimensional fit to each of M bc , ∆E, ∆t, CSMVA for B 0 → K 0 S π + π -γ. The fit is done using simulated data of 1 ab -1 . The combined probability distribution function is represented by the solid blue line while the two components are represented by a dotted green for BB background and dotted gray for continuum background.

D

  * + reconstruction D * + candidates are formed by combining D 0 and a soft π + , To demonstrate the selection cuts used for in the table for D * + , distributions of the mass difference ∆M (M D 0 π + -M D 0 ) for D * + candidates is shown in Fig 5.1 where the cut choice is taken according to the signal contributions in these distributions.

Figure 5 . 1 :

 51 Figure 5.1: Distribution of mass difference ∆M D * + = M D 0 π + -M D 0 for D * + candidates in simulated data.

Figure 5 . 2 :

 52 Figure 5.2: (left) R2 and (right) cos θ thrust distributions in simulated data

Figure 5 . 3 :

 53 Figure 5.3: Distribution of the number of events with multiple candidates at the end of the selection in simulated data .

Figure 5 . 4 :

 54 Figure 5.4: σ ∆t distribution for simulated data

Figure 5 . 5 :

 55 Figure 5.5: Projections of the 2-D fit to the signal MC sample for all the decay channels together: (left) M bc , (right) ∆E.

Figure 5 .Figure 5 . 6 :

 556 Figure 5.6: Projections of the 2-D fit to the bb MC sample for all the decay channels together: (left) M bc , (right) ∆E.

Figure 5 . 7 :

 57 Figure 5.7: Projections of the 2-D fit to the continuum MC sample for all the decay channels together:(left) M bc , (right) ∆E.

Figure 5 . 8 :Figure 5 . 9 :

 5859 Figure 5.8: Projections of the 2-D fit to the MC sample for all the decay channels together to extract the yields of the different components: (left) M bc , (right) ∆E. The combined probability distribution function is represented by the solid blue line while the three components are represented by a dashed red for the signal, a dotted purple for the bb background and a dashed-dotted orange for the continuum background.

Figure 5 . 12 :

 512 Figure 5.12: (left) Fit to the ∆t distribution of only continuum background events and (right) fit to the ∆t distribution of the sideband events in a full simulated data sample.

Figure 5 . 13 :

 513 Figure 5.13: Profile plot of the ∆t residual versus the true ∆t in the simulation. Error bars correspond to the uncertainty on the mean.

Figure 5 .Figure 5 . 15 :

 5515 Figure 5.15: Fit to residual for the signal sample in simulated data leaving all the parameters free.

Figure 5 . 16 :

 516 Figure 5.16: Fit to ∆t distribution of the simulated signal sample.

Figure 5 . 17 :

 517 Figure 5.17: Distribution of ∆t for the bb event contribution in the simulated data in the signal region.The superimposed fit follows the pdf defined in (5.6).

Figure 5 . 18 :

 518 Figure 5.18: Fit to ∆t distribution for all candidates in simulated data. The combined probability distribution function is represented by the solid blue line while the three components are represented by a dashed red for the signal, a dotted purple for the bb background and a dashed-dotted orange for the continuum background.

  fit on MC, Figure5.8

Figure 5 . 19 :

 519 Figure 5.19: Fit to the ∆t distribution of the sideband events in data.

Figure 5 . 20 :

 520 Figure 5.20: Fit to ∆t distribution for all candidates in data. The combined probability distribution function is represented by the solid blue line while the three components are represented by a dashed red for the signal, a dotted purple for the bb background and a dashed-dotted orange for the continuum background.

Figure 5 . 21 :

 521 Figure 5.21: Distribution of the difference with respect the true value of value of τ obtained with the procedure used on data obtained with a toy study. The blue dashed line indicates the mean of the distribution while 68.3% of the toys are contained between the red dashed-dotted lines.

Figure 5 . 22 :

 522 Figure 5.22: B 0 lifetime fit leaving τ e f f free.

Figure 5 .

 5 23 shows the difference of the SVD alignment constants used in this two data samples. Figure 5.24 and Table

Figure 5 . 23 :Figure 5 . 24 :

 523524 Figure 5.23: Difference of the SVD alignment constants between the alignment used in proc10 and the one used in proc9.

Figure 5 . 25 :Figure 5 . 26 :

 525526 Figure 5.25: Prospects of B 0 → K 0 S π 0 γ channel measured using 200 toy Monte Carlo experiments showing the statistical uncertainty of S and A parameters as function of the integrated luminosity planned for Belle II program. Belle and Babar statistical and systematical uncertainties from latest measurements for B 0 → K 0 S π 0 γ, S only parameter are also shown as dashed and full straight lines

Figure 5 . 27 :

 527 Figure 5.27: Total integrated daily luminosity and total integrated luminosity in fb -1 during Phase 3 2018-2020 data taking.

Figure 5 . 28 :

 528 Figure 5.28: Mid and long term peak and integrated luminosity plan of Belle II project, IR (Interaction Region) need to be upgraded in 2026.

Figure 5 . 29 :

 529 Figure 5.29: Une représentation schématique du l'accélérateur SuperKEKB

Figure 5 .

 5 [START_REF] Babu | Constraints on left-right symmetric models from the process b -> s gamma[END_REF] indique un aperçu schématique du collisionneur SuperKEKB. Le SuperKEKB vise une luminosité maximale de 8 × 10 35 cm -2 s -1 qui correspondent à une luminosité intégrée de 50 ab -1 , 40 fois plus grande que la luminosité produite à Belle.La principale nouveauté de l'amélioration de la luminosité du SuperKEKB est le schéma de nano faisceau, dans lequel la fonction verticale β au "point d'interaction" IP appelé β * y est réduite à environ 0.3 mm (20 fois moins de le KEKB) et l'angle de croisement du faisceau φ c a été augmenté d'un facteur de quatre environ par rapport à la KEKB. L'énergie asymétrique du faisceau, le Υ(4S), est produite avec une impulsion βγ, L'impulsion dépend de l'énergie des faisceaux et de l'angle de croisement entre eux. βγ est nécessaire pour mesurer la différence de temps entre les désintégrations des deux mésons B 0 produits sur le site Υ(4S), puisque ∆t = ∆z/βγ. Grâce à la réduction de l'asymétrie de l'énergie du faisceau à SuperKEKB, βγ est réduit d'un facteur 2/3 par rapport à KEKB. Ainsi, la distance moyenne ∆t (∆z dans la direction de l'impulsion) d'environ 190 µm à la KEKB, est réduite à environ 130 µm à la SuperKEKB.En raison de ces changements, le détecteur Belle II prendra des données à un accélérateur d'une luminosité 40 fois plus élevée, et doit donc être capable de fonctionner à des taux d'événements 40 fois plus élevés, avec des taux de fond plus élevés. Ainsi, afin d'améliorer les performances de Belle II, des modifications ont été apportées à la conception du détecteur. Le détecteur Belle II est conçu comme suit et comme présent dans la Figure5.30: détecteurs de suivi qui consiste en, PXD (détecteur de pixel), SVD (détecteur de vertex de bande de silicium), CDC(chambre de dérive centrale). Les détecteurs d'identification des particules qui consiste en, TOP(comptage de propagation de temps) dan la région de la barrel et ARICH (Le compteur d'aérogels) détecteur. Calorimètre électromagnétique ECL, mesurer le dépôt d'énergie des photons neutres à l'aide de

Figure 5 . 30 :

 530 Figure 5.30: Une représentation schématique du détecteur Belle II

Figure 5 . 31 :

 531 Figure 5.31: Les distributions de le S √ S+B en fonction des variables

Figure 5 .Figure 5 . 32 :

 5532 Figure 5.32: Fit to the z vertex residual for (left) the signal B and (right) the tag B.

Figure 5 . 33 :

 533 Figure 5.33: Fit to ∆t distribution for all candidates in data. The combined probability distribution function is represented by the solid blue line while the three components are represented by a dashed red for the signal, a dotted purple for the bb background and a dashed-dotted orange for the continuum background.

Chebychev(x) = 1 a ( 1 + c 1 x) 1 aFigure 34 :

 11134 Figure 34: Fits projection for B d → D -ρ + . The first two rows show the projections in (top) M bc and (middle) ∆E of the fits to the individual populations (left) signal, (center) bb background and (right) continuum background. The last row shows the projections in (left) M bc and (right) ∆E of fit to extract the yields of the individual components.

Figure 36 :Figure 37 :Figure 38 :Figure 39 :

 36373839 Figure 36: Fits projection for B d → D * -ρ + (D 0 → K -π + ). The first two rows show the projections in (top) M bc and (middle) ∆E of the fits to the individual populations (left) signal, (center) bb background and (right) continuum background. The last row shows the projections in (left) M bc and (right) ∆E of fit to extract the yields of the individual components.

Table 1 . 1 :

 11 Properties of force carrying bosons in the SM are half-spin particles satisfying the Fermi-Dirac statistics and the Pauli exclusion principle. They are further categorized as leptons or quarks. Leptons are particles that, if charged, interact both electromagnetically and weakly, if neutral only weakly. Quarks are the fermionic constituents of hadrons and then nuclei, they interact strongly, weakly and electromagnetically.

		Interaction	Mass(GeV/c 2 ) charge (e)
	Gluon	Strong	0	0
	Photon Electromagnetic W ± weak Z 0 weak	< 10 -24 80.38 ± 0.015 91.188 ±0.002	0 ± 1 0

  13 -s 12 c 23c 12 s 23 s 13 e iδ13 c 12 c 23s 12 s 23 s 13 e iδ 13 s 23 c 13 s 12 s 23c 12 c 23 s 13 e iδ 13 -c 12 c 23s 12 c 23 s 13 e iδ 13 c 23 c 13

  (1.13)

  .[START_REF] Wu | Experimental Test of Parity Conservation in β Decay[END_REF] For the B d mesons, the difference in width, ∆Γ B d , is expected to be small compared to Γ B d . Also one should note that ∆Γ B d ≪ Γ B d is model-independent. Moreover, the B d oscillation parameter x d has been measured[START_REF] Amhis | Averages of b-hadron, c-hadron, and τ-lepton properties as of summer 2016[END_REF]

	x d ≡	∆m d Γ B d	= 0.77 ± 0.004	(2.14)
	which implies then, model-independently, ∆Γ B d ≪ ∆m d . As a consequence one gets
		|Γ 12 | ≪ |M 12 |,	(2.15)
		|q/p| ∼ 1.	(2.16)

Table 4 .

 4 1.

	Categories Electron Intermediate Electron Muon Intermediate Muon	Targets for B 0 e -e + µ -µ

Table 4 . 2 :

 42 List of the selection cuts used for

Table 4 . 4 :

 44 CP violation parameters fitted from the four dimensional fit shown in Figures 4.10and 4.9

Table 4 . 5 :

 45 Table summarizing the different systematic sources and the systematic uncertainty assigned to each one, for the channel B 0 → K 0 S π 0 γ

	SVT Alignment	0.006		0.004
	Physics Parameters	0.0066		0.008
	Flavor tagging	0.005		0.002
	Fitting procedure	0.015		0.016
	Signal and Bkg fraction	0.00506		0.00680
	Resolution function	0.0016		0.0015
	CP from BB bkg	0.008		0.002
	Tag Side interference	0.001		0.015
	Total	0.02		0.024
	Source		∆ S	∆A
	Physics Parameters	0.002	0.001
	Flavor tagging		0.005	0.002
	Fitting procedure of ∆E, m es , Fisher discriminant Signal and Bkg fraction	0.02 0.01	0.023 0.008
	∆T fitting procedure and Resolution function	0.012	0.007
	Tag Side interference	0.001	0.015
	CP violation effect from BB background	0.008	0.002
	Total		0.027	0.03

Table 4 . 6 :

 46 Table summarizing the different systematic sources and the systematic uncertainty assigned to each one, for the channel

Table 4 . 7 :

 47 S parameter statistical uncertainty comparison between the current Belle II analysis on simulated data and Belle latest results on the two channels B 0 → K 0 S π + π -γ and B 0 → K 0 S π 0 γ, plus the expectations with the full Belle II planned data set of 50 ab -1 .

	-1 Belle statistical uncer-tainty	0.30 0.31	0.219 0.27
	Expected with Belle II 50 ab -1 uncertainty Belle II systematic uncer-tainty using 1 ab -1 Belle systematic uncer-tainty	0.04 0.02 0.07	0.03 0.027 +0.04 /-0.07

Table 5 .

 5

1: List of hadronic final states used to reconstruct B-meson decays.

Table 5 .3: Decay channels

 5

Table 5 . 4

 54

	3 7 8 10 11 All	2814 ± 0.0006 5.2811 ± 0.0005 5.285 ± 0.004 5.2820 ± 0.0009 5.27961 ± 0.00007 0.0087 ± 0.0017 0.00 ± 0.28 0.0070 ± 0.0008 0.68 ± 0.20 2.60 ± 0.27 0.0081 ± 0.0009 0.61 ± 0.20 3.23 ± 0.34 0.00206 ± 0.00029 0.00788 ± 0.00028 0.278 ± 0.025 0.796 ± 0.018 0.0069 ± 0.0015 0.0273 ± 0.0017 0.81 ± 0.05 1.11 ± 0.05 0.014 ± 0.004 2.0 ± 1.4 4.9 ± 1.6 0.0015 ± 0.0024 0.0244 ± 0.0029 0.67 ± 0.09 1.01 ± 0.09 0.0069 ± 0.0012 0.91 ± 0.34 2.6 ± 0.4 -0.002 ± 0.004 0.047 ± 0.006 0.70 ± 0.13 1.49 ± 0.15 3.4 ± 0.6 0.0017 ± 0.0006 0.0086 ± 0.0006 0.24 ± 0.05 0.85 ± 0.04 5.2842 ± 0.0027 0.014 ± 0.004 1.7 ± 1.1 5.6 ± 1.6 -0.0004 ± 0.0017 0.0268 ± 0.0020 0.49 ± 0.07 1.29 ± 0.08 5.28125 ± 0.00031 0.0078 ± 0.0005 0.64 ± 0.12 2.99 ± 0.19 0.00383 ± 0.00028 0.01200 ± 0.00032 0.580 ± 0.017 0.796 ± 0.014

: Fit parameters signal MC fits B 0 lifetime measurement analysis bb background distribution for M bc and ∆E

Table 5 . 5 :

 55 Fit parameters bb MC fits

	3 7 8 10 11 All	2900 ± 0.0014 0.0070 ± 0.0014 5.2900 ± 0.0006 0.0086 ± 0.0006 2.87 ± 0.30 2.61 ± 0.11 -0.0519 ± 0.0032 0.0600 ± 0.0019 2.7 ± 0.5 2.00 ± 0.16 -0.1784 ± 0.0027 0.0105 ± 0.0020 5.2896 ± 0.0018 0.0070 ± 0.0018 5.0 ± 2.6 4.1 ± 0.6 -0.011 ± 0.004 0.038 ± 0.004 5.2842 ± 0.0026 0.0035 ± 0.0017 2.2 ± 1.7 2.0 ± 0.6 -0.019 ± 0.005 0.0600 ± 0.0030 5.289 ± 0.014 0.0089 ± 0.0020 2.9 ± 1.4 2.9 ± 0.7 -0.034 ± 0.007 0.049 ± 0.014 5.288 ± 0.004 0.0072 ± 0.0015 2.7 ± 1.6 2.4 ± 0.7 -0.032 ± 0.006 0.060 ± 0.005 5.2900 ± 0.0006 0.0082 ± 0.0007 2.93 ± 0.09 2.58 ± 0.11 -0.012 ± 0.009 0.0316 ± 0.0032	-55 ± 7 -65 ± 4 -100 ± 5 -97 ± 4 (-1.2 ± 0.5) × 10 2 -125 ± 14 -65.3 ± 2.3	-2.93 ± 0.17 -3.72 ± 0.25 0.546 ± 0.014 0.31 ± 0.04 -2.7 ± 0.4 0.227 ± 0.022 -2.70 ± 0.33 0.273 ± 0.021 -2.0 ± 3.1 0.943 ± 0.030 -4.0 ± 0.9 0.69 ± 0.05 -2.84 ± 0.14 0.450 ± 0.010
	Channel	dµ [GeV]	s	dµ ′ [GeV]	s ′	f 1	f 2	f ′
	2 3 10 11 All	--0.1274 ± 0.0034 0.427 ± 0.019 --0.145 ± 0.009 0.62 ± 0.24 -0.142 ± 0.007 0.45 ± 0.06 -0.052 ± 0.013 3.00 ± 0.14	-----0.168 ± 0.009 0.78 ± 0.10 0.060 ± 0.022 0.472 ± 0.020 -----0.291 ± 0.012 --0.25 ± 0.04 --0.458 ± 0.026	0.030 ± 0.008 ----

Table 5 .6: Fit

 5

parameters continuum sample fits

Table 5 . 8 :

 58 Fit yields. The row Sum contains the sum of the yields of the individual modes, the raw All contains the yields considering together all the modes while the raw Data contains the result of the fit to the data. The columns pull i are defined as (n in true

	B 0 lifetime measurement analysis

i

)/σ n i .

Table

Table 5 . 13 :

 513 Comparison fit values fitting data of different reprocessing; proc10 corresponds to the same dataset as proc9+bucket7 but reconstructed with a better calibration and alignment.

Introduction

  Pour mon doctorant, je travaille sur l'expérience Belle II, qui enregistre les phénomènes produits par les collisions e + e -de l'accélérateur SuperKEKB situé au Japon. Le but de cette expérience est d'observer des processus non décrits par le Modèle Standard de la physique des particules. De tels signes expérimentaux seraient une découverte d'une physique nouvelle et donneraient accès, au moins partiellement, à la théorie dont le Modèle Standard est une version effective. L'un de ces nouveaux processus potentiel étudié dans notre groupe à l'IPHC, implique la restauration de la symétrie gauche-droite qui est rompue dans le modèle standard de la physique des particules et est également lié à l'asymétrie entre la matière et l'anti-matière observée dans notre univers. Il existe deux types de violation de la symétrie CP (combinaison des opérations de conjugaison de charge C et de renversement des coordonnées d'espace ou parité P) : une violation directe et une violation indirecte. La violation directe de CP est observée lorsque la probabilité d'une désintégration et celle du processus conjugué par CP sont différentes, tandis que la violation indirecte se produit lorsque l'amplitude complexe de désintégration des particules et des antiparticules dans le même état final diffèrent. Dans mon travail de thèse, j'utilise une technique qui donne accès aux deux paramètres de la violation de CP, S pour la violation indirect et C pour la violation directe. L'une des désintégrations intéressantes où la violation de CP serait un moyen de révéler l'existence de nouvelles particules est la désintégration radiative des méson B 0 qui se produit à travers des boucles quantiques, où des particules lourdes peuvent se propager. Le Modèle Standard, du fait de la structure vecteur-axial du couplage de l'interaction faible, prévoit que les photons émis dans ces désintégrations sont polarisés : principalement gauchers pour les mésons et droitiers pour les anti-mésons. L'état final étant différent pour les mésons et les antimésons, il ne peut y avoir de violation de CP indirecte. Certains modèles de nouvelle physique introduisent des contributions de particules lourdes à ces désintégrations radiatives détruisant la polarisation différenciée entre méson et anti-méson de sorte que la violation indirecte peut se produire. Une telle observation représenterait à la fois une invalidation concrète du Modèle Standard et la découverte d'une nouvelle source de violation de CP.Au sein du groupe strasbourgeois, je travaille sur la mesure des paramètres de violation de CP indirecte et directe S et C respectivement dans la transition radiative b → sγ qui se produit à travers des boucles quantiques. Nous étudions cette transition à travers deux états finals B 0

  R sig , et P bkg . Ensuite, nous construisons une fonction de vraisemblance et nous la maximisons pour obtenir les meilleures estimations pour A et S. A fin d'extraire S et A, plusieurs étapes doivent être réalisées la sélection des événements, PremièrE, pour chaque événement l'évaluation des temp de désintégrations et de la nature méson ou anti-méson de la désintégration, ensuite une inférence statistique des paramètres de CP sur l'ensemble des événements sélectionnés et enfin l'évaluation de l'incertitude associée aux effets systématiques sur la mesure.

.7) P bkg (∆t) est la PDF decrivant la ∆t distribution des candidats de fond, et R sig (∆t) ∆t fonction de résolution pour les candidats de signal. Afin d'obtenir des valeurs non biaisées des paramètres CP, il est important de bien comprendre et d'estimer f sig , w, ∆w,

Table 5 . 14 :

 514 Différentes incertitudes systématiques contribuent à la mesure des paramètres quantifiant la violation de CP, S et C. La contribution dominante est liée à la procédure d'ajustement des distributions temportelles. En effet, de nombreux paramètres sont utilisés dans la modélisation de ces distributions et, lors de l'ajustement final des données, ces paramètres sont fixés à partir des données simulées. J'ai développé une procédure d'évaluation de l'incertitude induite sur les valeurs S et C par l'incertitude sur les paramètres fixés de l'ajustement. La méthode consiste à faire varier individuellement tous ces paramètres dans un intervalle fixé par l'incertitude sur leur estimation, puis à refaire l'ajustement global. La distribution des valeurs de S et C trouvées permet alors de quantifier l'incertitude systématique de l'ordre de ∆S sys = 0.02 pour S par exemple. Ces effets systématiques sont beaucoup plus faibles que l'incertitude statistique, qui elle atteint ∆S stat = 0.2. Comparaison de l'incertitude statistique des paramètres entre l'analyse actuelle de Belle II sur les données simulées et les derniers résultats de Belle sur les deux canauxB 0 → K 0 S π + π -γ et B 0 → K 0 S π 0 γ,plus les attentes avec l'ensemble complet des données prévues de Belle II de 50 ab -1 . pour les mêmes canaux. Les résultats de Belle II sont similaires ou légèrement meilleurs que celles de Belle. C'est une découverte importante, qui démontre que le nouveau détecteur de vertex Belle II a la capacité, dans la simulation, de surmonter la pénalité de la faible poussée disponible dans SuperKEKB par rapport à celle qui prévaut à KEKB-Belle. Le prochain chapitre explorera l'état actuel du vertex dans Belle II avec une mesure sur des données réelles. En ce qui concerne les attentes relatives à l'ensemble des données de Belle II, soit 50 ab -1 , il semble que la mesure sera encore statistiquement limitée. Bien entendu, il s'agit d'une enquête préliminaire sur les performances de l'expérience Belle II. Des outils d'analyse plus avancés sont déjà développés et ils augmenteront naturellement la puissance statistique des mesures TDCPV.

	x

Conclusion de l'analyse TDCPV:

Une comparaison est faite avec les incertitudes statistiques réalisées par Belle. Le tableau 5.14, rapporte les incertitudes statistiques obtenues dans cette analyse en utilisant les données simulées de Belle II de 1 ab -1 et les incertitudes obtenues de la dernière analyse de Belle

Mesure du temps de vie des mésons B 0 avec les premières données Dans

  ce chapitre, une nouvelle analyse complète est présentée, la mesure de la durée de vie B 0 . Comme déjà révélé dans le chapitre 4, dans la mesure TDCPV, le vertex est la clé pour augmenter la sensibilité à l'analyse temporelle. Pour démontrer la capacité de vertexing dans Belle II, une analyse qui mesure la mesure de la durée de vie B 0 , τ en utilisant la différence de temps mesurée entre les deux paires B 0 et B 0 sera un outil pour vérifier les outils d'ajustement des vertex et la modélisation de la résolution temporelle. Cette mesure est effectuée en utilisant l'ensemble de données de la phase 3 précoce et les désintégrations hadroniques du méson B. Nous suivons une procédure d'analyse standard qui présente des similitudes avec l'analyse TDCPV. Comme pour l'analyse TDCPV, le candidat méson B est entièrement reconstruit mais avec des états finaux de désintégration hadronique[START_REF]Precise Measurement of B Meson Lifetimes with Hadronic Decay Final States[END_REF].La technique du reste de l'événement permet de reconstruire la position du xi sommet de l'autre méson B, toujours appelé tag side même s'il n'est pas utilisé pour le marquage comme c'est le cas dans l'analyse TDCPV. La méthode d'estimation de la fraction du signal est similaire à celle utilisée dans l'analyse TDCPV, en utilisant un ajustement 2D aux distributions M bc et ∆E. Le paramètre de durée de vie τ est mesuré en utilisant un ajustement à une dimension de la distribution du temps. Chacune des trois distributions du temps, pour le signal, le continuum et le fond bb, est modélisée. Une fonction commune a également été développée pour le modèle de résolution temporelle, en ajustant les paramètres spécifiquement pour chaque contribution. La forme fonctionnelle du modèle de résolution est définie pour être simple car il s'agit de la première modélisation au démarrage de l'analyse de Belle II. Toute mesure officiel de la collaboration Belle II suit une procédure |"à l'aveugle". C'est à dire que la méthode est mise au point entièrement sur des données simulées, puis après validation d'un comité de revue, elle est appliquée au données réelles.

The existence of a fourth quark, c, was suggested in 1964 for symmetry reasons related to strong interaction. In 1970, the GIM mechanism that suppresses Flavour Changing Neutral Currents (FCNC) was discovered, involving the introduction to the fourth quark flavour, charm, that was discovered soon after, in(1974).

The flavor eigenstates of the neutral B meson are defined as B 0 = bd and B 0 = db

In fact, the two beam collides with a very small angle of 83 mrad or 4.76 degrees, which is neglected in this analysis and the beam is assumed to follow the z-axis.

Acknowledgements

Lifetime extraction method

To measure B 0 lifetime from the selected candidates, an unbinned likelihood fit is performed on the overall ∆t distribution. The probability distribution in equation (5.8) describes this overall distribution by combining the contribution yields measured in Section 5.4.

P all (∆t) = n sgn P sgn (∆t) + n bb P bb (∆t) + n cont P cont (∆t).

(5.

2)

The ∆t distribution analytical models for the three main contributions to the candidate sample are described in section 5.5.1. The fits to ∆t corresponding to each component is also shown. In section 5.5.2, the full ∆t fit on simulated data using the model in equation 5.8 is presented as well parameters used and extracted from this fit. In section 5.5.3, the continuum modeling study on data is discussed. Finally, the lifetime full fit on real data is shown in section 5.6.

An important ingredient of the fit to extract the B lifetime is the resolution function R that describes the smearing introduced by various effects during the reconstruction. In this analysis R is modeled by the sum of three Gaussian distributions (5.9).

R(δ

A universal resolution function is used and not a candidate-by-candidate one, depending for example on the uncertainty on ∆t due to the small sample size considered in this analysis.

Modeling of ∆t component for the three components

Continuum background and ∆t distribution P cont Background candidates coming from light continuum events are not expected to display any specific time behavior. Their distribution can thus be described with same functional form than the resolution of equation (5.9): a sum of three Gaussian distributions. The candidates coming from cc events, that are considered in the continuum background, contain D ( * ) mesons which have a sizeable lifetime. However as the background coming from this sample is combinatorial in nature (there are no real B 0 so the D ( * ) mesons are associated with particles with the other side of the event) and the sample size considered is limited, three Gaussian distribution still provides a good description of the full combinatorial background as will be see by the goodness of the fit obtained. The fit of the ∆t distribution to a MC sample of continuum-events candidates is shown in Figure 5.12. Another fit is performed to a sideband designed to be dominated by continuum background defined by selecting M bc < 5.26 GeV/c 2 and |∆E| < 0.1 GeV and inverting the continuum background selection to R 2 > 0.4 and cos θ thrust > 0.8. In this region only 1% contamination from bb candi- dates is expected and there is a good agreement between the fit to the continuum sample selected using MC information and the fit to the sideband.

In the final fit (5.8) all the parameters of P cont , the probability distribution function describing the continuum component, will be fixed from this sideband fit. This will be also be the strategy for the fit on data. There however, due to the limited sample size, only µ 1 and σ 1 will be left free in the data sideband fit while the others will be fixed to the value from the MC sideband fit. More details on the fit to the continuum ∆t fit on data can be found in Section 5. for the signal. This effect is caused by the fact that on the signal side we have exclusive decays where the fitter TreeFitter takes correctly into account the charm meson lifetime since it simultaneously fits an entire decay chain. On the tag side, the inclusive decay of the other B is with Rave. A method to reduce the contributions from secondary decays is implemented in Rave, this method however is not perfect and leads to a bias toward larger lifetimes for the tag B that, as the signal B is unbiased, converts into a negative bias for ∆t.

Parameter

Signal side Tag side Figure 5.15 shows the fit to the residuals of ∆t leaving all the parameters free. From this fit, one can calculate σ ∆t = (weighted sum of the sigmas of each contributions) ∼ 1.1 ps. Similarly, one can calculate the resolution on the signal side vertex: σ z sgn = (weighted sum of the sigmas of each contributions from table 5.10) ∼ 30 µm and for tag side: σ z tag ∼ 80 µm.

A fit is performed to extract the lifetime (Figure 5.16) on signal events. The only free parameters will be the lifetime itself and µ 1 and σ 1 of the resolution function while the other parameters can be fixed from the fit to the ∆t distribution for the continuum events as shown in Figure 5.12. One can notice that the obtained value for the B 0 lifetime is compatible with the known one.

Two dimensional fits get signal and background fractions for channels