Jacques Soffer

Bernd Surrow

Claude Bourrely

Transverse double-spin asymmetries for electroweak gauge-boson production in high-energy polarized p ↑ + p ↑ collisions

Keywords: Gauge boson production, Statistical distributions, Asymmetries

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Transverse double-spin asymmetries for electroweak gauge-boson production in high-energy polarized p ↑ + p ↑ collisions

Introduction

The collision of high-energy polarized proton beams with a center-ofmass energy of √ s = 200 GeV and √ s = 510 GeV at the Relativistic Heavy-Ion Collider (RHIC) at Brookhaven National Laboratory (BNL) provides a powerful way to gain a deeper insight into the spin structure and dynamics of the proton such as the study of the helicity distributions of gluons and quarks/antiquarks based on well established high-energy QCD and W boson processes, respectively [1,2,3,4]. Several studies have been suggested in the past to gain a better understanding of the quark transversity distribution, in particular the measurement of the transverse double-spin asymmetries (A T T ) for W and Z production [5]. At lowest-order (LO) it was found that A T T = 0 for W production and the estimate of A T T for Z production was done by assuming that the transversity distributions h q 1 (x) coincide with the helicity distributions ∆q(x), similarly for antiquarks. This simplification is valid for a proton at rest, in the absence of relativistic effects, but in general these distributions are different. Among the three fundamental distributions of twist-2 are the unpolarized quark distributions q(x), the quark helicity distributions ∆q(x) and the quark transversity distributions h q 1 (x). Transversity distributions are the least known because it suffers from the lack of experimental information. The distributions h q 1 (x) are chiral odd and therefore they are not directly accessible in Deep Inelastic Scattering (DIS). Since there is no gluon transversity distribution in a nucleon, the quark transversity distribution has a pure non-singlet Q 2 evolution. Several years ago [6], the following positivity bound

q(x) + ∆q(x) ≥ 2|h q 1 (x)|, (1)
(similarly for antiquarks), was obtained at LO. Later [7,8,9], this strong result was proven to be valid after Q 2 evolution, up to next-to-leading order (NLO). The transverse double-spin asymmetry is defined as A T T = (dσ ↑↑ -dσ ↑↓ )/(dσ ↑↑ + dσ ↑↓ ), where σ ↑↑ (σ ↑↓ ) denotes the cross section with the two initial protons transversely polarized in the same (opposite) direction. This physics observable was considered earlier for high-p T jet and direct photon production and was estimated at RHIC energy at the 10 -3 level [10]. The same order of magnitude was obtained later for upper bounds on A T T , by saturating the transversity distributions, at low scale by the positivity bound Eq. ( 1) [11]. The experimental finding of large asymmetries would constitute one more spin puzzle and it is also very challenging in the case of gauge boson production. In view of the 2017 running operation at RHIC of transversely polarized proton beams and the fact that the reconstruction of W and Z bosons is well established at mid-rapidity by the STAR collaboration [12], we thought it is timely to revisit this subject.

In this letter, we will extend the discussion beyond the LO case for the prediction of A T T = 0 for W production. The main purpose is to present a NLO calculation of the allowed maximal A T T for Z production, using Eq. ( 1). We will also give some experimental details concerning the future measurement of these asymmetries, as well as the expected accuracy.

Transverse double-spin asymmetry for gauge boson production and quark transversity distributions

For gauge boson production, assuming that the underlying parton subprocess is quark-antiquark annihilation, we easily find at LO

A T T = âTT × i=u,d (b 2 i -a 2 i ) h q i 1 (x 1 )h qi 1 (x 2 ) + (x 1 ↔ x 2 ) i=u,d (a 2 i + b 2 i ) [q i (x 1 )q i (x 2 ) + (x 1 ↔ x 2 )] . ( 2
)
Here âTT is the partonic transverse double-spin asymmetry, given in Ref. [14], which reads âTT = sin 2 θ cm cos 2φ cm 1 + cos 2 θ cm ,

a simple expression in terms of θ cm and φ cm , the polar and azimuthal angles of one charged lepton momentum with respect to the beam and the proton polarization, respectively. Clearly âTT = 1, its maximum value, is obtained when θ cm = π/2 and φ cm = 0. However in order to increase the observable events rate, one should integrate over the angles and one gets âTT = 1/π. In order to extend Eq. ( 2) to NLO, one has to introduce the NLO transversity distributions h q 1 (x, Q 2 ) and to replace âTT , by its NLO expression âTT (O(α s )), following the results of Ref. [15]. In Eq. (2) a i and b i denote the vector and axial-vector coupling constants of q i to the produced gauge boson. This result generalizes the case of leptonpair production, i.e. Drell-Yan production, through an off shell photon γ and corresponding to b i = 0 and a i = e i , the electric charge of q i . For W ± production, which is purely left-handed, we expect A T T = 0, since in this case a 2 i = b 2 i . This strong result which is valid beyond LO (see Appendix) is worth checking experimentally. It follows from the fact that one assumes a universal V -A coupling. The observation of a non-zero A T T , could be the footprints of new physics at high scales, beyond the Standard Model. NLO corrections to the above expression Eq. ( 2) have been calculated [9] and they gave estimates of the maximal A T T for Drell-Yan dimuon production of mass M . Upper bounds on A T T as function of the dimuon rapidity, for M = 5 -20GeV, much below the Z peak, were also obtained [15].

We will now summarize what is known about the transversity distributions, from two different methods of indirect extraction. Transversity can be extracted in the standard framework of collinear factorization using SIDIS with two hadrons detected in the final state. In this case, the distribution h q 1 (x) is multiplied by another specific chiral-odd Di-hadron Fragmentation Function (DiFF), which can be extracted from the corresponding e + e -annihilation process leading to two back-to-back hadron pairs. In the collinear framework, evolution equations of DiFFs can be computed and in particular, in Ref. [16] they have considered the recent measurement from the COMPASS collaboration for identified hadron pairs produced off transversely polarized proton targets [START_REF] Braun | COMPASS results on the transverse spin asymmetry in hadron-pair production in SIDIS[END_REF]. By combining proton and deuteron data, COMPASS has managed to perform the flavor separation h u 1 (x) and h d 1 (x). The error analysis is performed with the so-called replica method based on the random generation of a large number of replicas of the experimental points. As such, this method allows for a more realistic estimate of the uncertainty on DiFFs, so the results shown in Ref. [16] represent certainly the currently most realistic estimate of the uncertainties on the valence transversity distributions (see Fig. 8 of [16]).

Transversity can be also extracted using another method involving transverse momentum dependent (TMD) PDFs, in particular the Collins fragmentation function. Assuming TMD factorization, the Collins fragmentation function (FF) can be studied in SIDIS experiments, where it appears to be convoluted with the transversity distribution h q 1 (x, p T ) depending on p T , which is now considered as a TMD PDF. It induces an asymmetry, the so-called Collins azimuthal asymmetry, which has been clearly observed experimentally. The Collins FF also induces azimuthal angular correlations between hadrons produced in opposite jets in e + e -annihilation. Consequently, a simultaneous analysis of SIDIS and e + e -data allows the combined extraction of the transversity distributions and the Collins FFs. The most recent results of this method can be found in Refs. [18,19]. 1 (x, Q 2 ) (q = u, d), from the PDFs set of BS15 [13], as a function of x, at the initial scale

0.2 0.4 d ū u d Q 2 = 1 GeV 2 Q 2 = 10 GeV 2 Q 2 = 1 GeV 2 Q 2 = 10 GeV 2 xh u 1 (x, Q 2 ) xh d 1 (x, Q 2 ) xh u 1 (x, Q 2 ) xh d 1 (x, Q 2 ) xh d 1 (x, Q 2 ) xh ū 1 (x, Q 2 ) xh d 1 (x, Q 2 ) xh ū 1 (x, Q 2 ) x x
Q 2 = 100 GeV 2 Q 2 = 100 GeV 2 xh d 1 (x, Q 2 ) xh d 1 (x, Q 2 ) xh u 1 (x, Q 2 ) xh u 1 (x, Q 2 ) xh d 1 (x, Q 2 ) xh ū 1 (x, Q 2 ) xh d 1 (x, Q 2 ) xh ū 1 (x, Q 2 ) x x x x Q 2 = M 2 Z Q 2 = M 2 Z 0. 2
Q 2 = 1GeV 2 , Q 2 = 10GeV 2 , Q 2 = 100GeV 2 and at Q 2 = M 2
Z , after QCD NLO evolution. (right) Same for antiquark transverse distributions. Note that they are equal for ū and d, which is a consequence of an approximate equality of the potentials X - u = X - d in the BS model, as found in Ref. [13] and earlier works.

Their fit results are compatible (see Fig. 6 of Ref. [18] and Fig. 3 of Ref. [19]) and one finds that for Q 2 = 2.4GeV 2 , h u 1 (x) > 0 has a maximum of 0.3 for x near 0.4 and h d 1 (x) < 0 has a maximum of -0.15 for x near 0.1. For the down quark the tranversity tends to saturate the positivity bound, for x > 0.2. We emphasize the fact that nothing is known for antiquarks transversity. Our purpose is to present a NLO calculation of the allowed maximal A T T for Z production, using Eq. ( 1) to construct the maximal bound for quark (antiquark) transversity distributions h q 1 (x, Q 2 ) (q = u, d), from the PDFs set of BS15 [13]. In Fig. 1 we display these distributions which saturate the positivity bound at the initial scale Q 2 = 1GeV 2 and at Q 2 = M 2 Z , after QCD NLO evolution. We observe a rather strong reduction at this high energy scale. They will be used to calculate the allowed maximal A T T for Z production at RHIC at BNL and the results are given in the next section, together with the expected accuracy on this measurement. Finally let us also mention recent lattice-QCD results [20] on the isovector transversity distribution x[h u 1 (x)h d 1 (x)] [20], using the large-momentum effective field theory (LaMET) approach. It leads to a surprising large result in the large-x region and to some insight into the corresponding antiquark quantity (see Fig. 6 of Ref. [20]).

Results

The production of Z bosons in polarized proton collisions at √ s = 500 GeV has been demonstrated in a proof-of-principle measurement by the STAR collaboration [12]. The measurement of the total cross-section is based on an integrated luminosity of 13.2 pb -1 of a data sample collected in 2009 with an estimated total efficiency of tot = 0.338 ± 0.012 (stat.) ± 0.021 (sys.). We denote by η and E T the pseudorapidity and the transverse energy of a charged lepton in the Z/γ * → e + e -production. The total number of observed events in the mid-rapidity region of |η| < 1, E T > 15 GeV and an invariant e + e -mass window cut of 70 < m inv < 110 GeV amounts to 13 ± 3.6 with a small background contribution of 0.1 ± 0.1 (stat.) +1.3 (sys.) -0.0 (sys.) . The fiducial cross-section is given by σ f id Z/γ * • BR(Z/γ * → e + e -) = 2.9 ± 0.8 (stat.) +0.2 (sys.) -0.3 (sys.) ± 0.4 (lumi) pb which translates into a total cross-section of σ tot Z/γ * • BR(Z/γ * → e + e -) = 7.7 ± 2.1 (stat.)

+0.5 (sys.) -0.9 (sys.) ± 1.0 (lumi) pb taking into account acceptance corrections for fidicial and kinematic requirements. This measured cross-section agrees within uncertainties with a quoted theoretical predication of 10.8 pb at NLO level based on the unpolarized PDF set of MSTW08 [12]. A larger data sample taken in 2011 and 2012 of 86 pb -1 was used to measure the first longitudinal single-spin asymmetry A L for Z/γ * → e + e -production for |η| < 1, E T > 14 GeV and an invariant e + e - mass window cut of 70 < m inv < 110 GeV [1]. The measured asymmetry of A Z/γ * L = -0.07 +0. 14 -0.14 is consistent within the large uncertainties with NLO calculations based on different helicity-dependent parton distribution functions.

The measurement of both W and Z production is well established at mid-rapidity by the STAR experiment. The phase space cuts which will be used for determining A T T for Z/γ * → e + e -are based on the STAR selection cuts of |η| < 1, E T > 15 GeV and an invariant e + e -mass window cut of 70 < m inv < 110 GeV. Figure 2 shows the E T , η and m inv distributions for Z/γ * → e + e -production with the characteristic Jacobian peak for Z production at roughly half of the Z boson mass in the E T distribution and a peak at the mass of the Z boson in the m inv distribution. These NLO distributions have been determined using a NLO MC framework by D. de Florian and W. Vogelsang [21] allowing the calculation of various differential distributions at NLO level. The Z boson rapidity distributions with and without STAR selection cuts are shown in Figure 3. Note that we have the symmetry property dσ/dy Z (y Z ) = dσ/dy Z (-y Z ). Extensions of the measurable η coverage for e + /e -would be advantages to increase the y Z = (1/2)(η e + + η e -) coverage.

The measurement of A Z/γ * T T is expected to be performed using the same selection criteria of |η| < 1, E T > 15 GeV and an invariant e + e -mass window cut of 70 < m inv < 110 GeV. These cuts have therefore been used for a p s = 510 GeV full NLO calculation. The unpolarized cross-section has been determined using the PDFs set of BS15 [13]. Figure 4 displays the maximal bound as a function |y Z | shown as a shaded band for the transversity distributions used in the calculation of A T T . Note that A T T (y Z ) = A T T (-y Z ). The respective LO result is very similar suggesting that NLO corrections are in fact rather small. The maximal bound is compared to two running scenarios at RHIC in 2017 of 400 pb -1 and a potential long run beyond 2020 of 1000 pb -1 assuming a beam polarization of 60%. The uncertainties on A T T for Z production have been evaluated using the projected 2017 and beyond 2020 luminosities, beam polarization values at RHIC together with published experimental efficiencies for Z production [12]. Systematic uncertainties for double-spin asymmetries are expected to be much smaller [2,22].

A measurement of a A T T for Z production would provide the first direct constrain of transversity distributions. The sensitivity for A T T for W boson production has been also estimated. The uncertainties of A T T for W + / W - boson production at 400 pb -1 (1000 pb -1 ), amount to 0.015 / 0.024 (0.009 / 0.015), assuming also a beam polarization of 60%, taking into account published experimental efficiencies for W + / W -boson production [12]. The observation of a statistically significant non-zero A T T for W production would violate expectations within the Standard Model.

q 1 (x)| max = 1 2 (q(x) + q(x)) |h q 1 (x)| max = 1 2 (q(x) + q(x))

Summary

We have emphasized the relevance of measuring the transverse doublespin asymmetries A T T in the production, at mid-rapidity, of W and Z/γ * gauge bosons in polarized proton-proton collisions at a center-of-mass energy √ s = 510GeV. For W production A T T = 0 beyond LO is a very strong result. It will be checked for the first time in the 2017 run at RHIC at BNL. We have also presented a QCD NLO calculation of the allowed maximal A T T for Z production, by saturating Eq. ( 1) to construct the maximal bound for quark (antiquark) transversity distributions h q 1 (x, Q 2 ) (q = u, d), from the PDFs set of BS15 [13]. Although the experimental uncertainty in this case is larger, due to a much lower production rate and the limited acceptance of STAR, this will be the first attempt to extract directly transversity distributions from hadronic collisions, in particular for antiquarks barely unknown. The situation is better with long-term prospects beyond 2020 at RHIC. Finally, in addition to the Drell-Yan production mechanism involving only transversity distributions, so far considered, there could be other terms in-volving the product of TMD parton distributions, called double Sivers effect or double worm-gear effect [23]. They require a non-zero low transverse momentum for the gauge boson and the corresponding transverse double-spin asymmetries are expected to be very small.

Figure 1 :

 1 Figure1:(left) Maximal bounds for quark transverse distributions h q 1 (x, Q 2 ) (q = u, d), from the PDFs set of BS15[13], as a function of x, at the initial scaleQ 2 = 1GeV 2 , Q 2 = 10GeV 2 , Q 2 = 100GeV 2 and at Q 2 = M 2Z , after QCD NLO evolution. (right) Same for antiquark transverse distributions. Note that they are equal for ū and d, which is a consequence of an approximate equality of the potentials X - u = X - d in the BS model, as found in Ref.[13] and earlier works.

Figure 2 :

 2 Figure 2

  Figure 3

Figure 3 :

 3 Figure 3: Differential NLO cross-section of Z boson rapidity as a function of y Z , blue shade with no cuts, red shade with specific cuts.

Figure 4 :

 4 Figure 4: Maximal bound of A T T as a function of |y Z | shown as a band in comparison to uncertainty estimates for two running scenarios at RHIC in 2017 of 400 pb -1 and a potential long run beyond 2020 of 1000 pb -1 assuming a beam polarization of 60%.

Acknowledgments

We are grateful to W. Vogelsang for clarifying several points of this work and for providing a useful code to make some calculations. We also express our sincere gratitude to D. de Florian for providing help with the unpolarized NLO Z production code. We greatly appreciate interest and encouragement from A. Metz at an earlier stage of this work.

Appendix

Here we present a simple proof that A T T = 0 beyond LO, for W production. At LO in the Drell-Yan picture one has the quark-antiquark fusion reactions q(p 1 , s 1 ) + q(p 2 , s 2 ) → W , where p 1 , p 2 are the four-momenta of q and q, s 1 , s 2 their corresponding spin pseudo-vectors. The matrix element describing the above transition, assuming a universal V -A coupling, is M = ūq (p 1 , s 1 )γ µ (1γ 5 )u q(p 2 , s 2 )W µ , where u(p, s) is the four-components spinor u(p, s). The projection operator onto a state of definite spin s is u(p, s)ū(p, s) = 1/2(p / + m)(1 + γ 5 s /), using the Feynman slash notation defined as k / = γ µ k µ . The factor (1γ 5 ) in M stands for the fact that the W are left-handed. For the transverse double-spin asymmetry A T T , one needs to take a transverse spin vector s T and, in the massless case, the cross section

If one moves to the left, the most right (1γ 5 ) factor, it reaches the other (1γ 5 ) factor after three sign changes and becomes (1 + γ 5 ), so it is obvious that this trace is zero. Now at NLO one can start radiating a gluon. The gluon is a vector particle, so one adds another γ α to the trace and also a quark propagator p /. The sign changes survives, the trace still vanishes and this is true for as many gluons as one wants. In the case of the double helicity asymmetry A LL , one uses the projection operator onto a state of definite helicity, u(p, h)ū(p, h) = 1/2(p / + m)(1 + γ 5 h), so clearly one does not get zero.


Charles Moisset

Antoine Bourgade

Julien Lumeau

Fabien Lemarchand

Carine Perrin-Pellegrino

Hassan Akhouayri

Jean-Yves Natoli

Konstantinos Iliopoulos
email: konstantinos.iliopoulos@fresnel.fr

Saturable absorption optimization of silica protected thin Sb2Te3 layers towards super-resolution applications

Keywords: Nonlinear optical response, Nonlinear absorption, Chalcogenides, Z-scan, Super-resolution

Introduction

Currently there is a growing interest for optical inscription of nano-objects inside materials. Surpassing the diffraction limit however imposes several difficulties and different methods have been suggested in order to achieve that, as for example X-Ray lithography [1].

However such techniques require complicated experimental procedures and high cost equipment. Recently Stimulated Emission Depletion (STED) has been combined with direct laser writing, providing a high resolution (55 nm) [START_REF] Wollhofen | 120 nm resolution and 55 nm structure size in STED-lithography[END_REF]. In this case a complex experimental setup has been required.

Another way to surpass the diffraction limit is to use the nonlinear absorption and/or the nonlinear refraction [START_REF] Wei | Nano-optical information storage induced by the nonlinear saturable absorption effect[END_REF][START_REF] Wei | Laser beam induced nanoscale spot through nonlinear "thick" samples: A multi-layer thin lens self-focusing model[END_REF]. Both processes can result to a decrease of the size of a focused Gaussian beam by the material itself. In the case of the nonlinear refraction a self-focusing of the material is needed. Concerning the nonlinear absorption, a saturable absorption is required, which provides a decrease of the transmittance by decreasing the laser intensity. In this way the low-intensity part of the beam is absorbed resulting to a decrease of the beam size. The resolution enhancement can be in principle further improved by combining twophoton processes [START_REF] Iliopoulos | Reversible Two-Photon Optical Data Storage in Coumarin-Based Copolymers[END_REF][START_REF] Spiridon | Novel pendant azobenzene/polymer systems for second harmonic generation and optical data storage[END_REF]. This approach can be very promising for a variety of applications including waveguiding, integrated spectroscopy, frequency converting in the nanoscale, as well as optical data storage.

The main difficulty of using the nonlinear optical (NLO) response of materials for super-resolution is the necessity of high optical nonlinearities. Thin films based on the chalcogenide material Sb 2 Te 3 can be very promising candidates as they can exhibit a very high saturable absorption [START_REF] Wei | Nano-optical information storage induced by the nonlinear saturable absorption effect[END_REF][START_REF] Liu | Nonlinear absorption of Sb-based phase change materials due to the weakening of the resonant bond[END_REF]. However an optimization of their structure is necessary in order to achieve the desirable nonlinearities. Few reports exist concerning the NLO response of the Sb 2 Te 3 material [START_REF] Wei | Nano-optical information storage induced by the nonlinear saturable absorption effect[END_REF][START_REF] Liu | Nonlinear absorption of Sb-based phase change materials due to the weakening of the resonant bond[END_REF][START_REF] Liu | Origin of the giant optical nonlinearity of Sb 2 Te 3 phase change materials[END_REF], there is consequently no sufficient understanding of the relation between its structure, the laser excitation parameters and the nonlinear optical response. In this work we provide a detailed presentation of Sb 2 Te 3 thin films deposition and postpreparation, aiming to enhance the optical nonlinearities. Then their NLO response is studied by the Z-scan technique [START_REF] Iliopoulos | Ultrafast third order nonlinearities of organic solvents[END_REF][START_REF] Sheik-Bahae | Sensitive measurement of optical nonlinearities using a single beam[END_REF] both at the IR (1064 nm) and the visible (532 nm) parts of the spectrum.

Experimental part

Firstly, thin Sb 2 Te 3 films have been deposited on B270 multicomponent silicate glass substrates by the electron beam deposition technique (Bühler SYRUSpro 710), at room temperature, with a rate of 0.5 nm/s and using pure Sb 2 Te 3 glass targets. Two different series of thin films, having different thicknesses have been deposited. The thickness of each set of films has been measured by local removal of the thin film layer and then performing Atomic Force Microscopy measurements. The thicknesses of the two sets of thin films have been found to be 200 nm and 24 nm respectively. A relatively high thickness has been chosen for the first set of films in order to provide a significant signal, during the XRD studies and thus a higher accuracy. A set of thinner films (24 nm thickness) has been prepared for the NLO studies in order to increase the compatibility with super resolution applications. This is due to the fact that for Super-Resolution applications steep focusing is required providing short Rayleigh lengths. Moreover a low thickness provides a higher sample transmittance, which is beneficial for applications.

A 10 nm thick silica layer has been deposited in all cases over the Sb 2 Te 3 , in the same chamber, immediately after the deposition of the latter, in order to avoid critical oxidation of the material during the annealing. Different strategies could be followed in order to avoid oxidation, as for example heating in vacuum or in gas atmosphere [START_REF] Liu | Origin of the giant optical nonlinearity of Sb 2 Te 3 phase change materials[END_REF][START_REF] Fujimori | Crystallization process of Sb-Te alloy films for optical storage[END_REF][START_REF] Park | Optical properties of (GeTe, Sb 2 Te 3 ) pseudobinary thin films studied with spectroscopic ellipsometry[END_REF]. However adding a thin silica layer appeared as a more efficient approach as it can protect the thin films even after the annealing. Moreover it can allow laser annealing of the samples under air, which can be useful in several cases. Another advantage of using silica as protecting layer, is its transparency at the VIS-NIR region of the spectrum and its negligible NLO response, compared with chalcogenide glasses [START_REF] Olivier | Nanosecond Z-scan measurements of the nonlinear refractive index of fused silica[END_REF].

The XRD studies have been carried out with a theta-theta configuration and CuK radiation by in-situ annealing. The annealing has been carried out in an Anton Paar chamber under air.

In order to measure the third order nonlinear optical parameters of thin film layers a Zscan setup has been built. The Z-scan technique is based on the measurement of the transmission of a thin sample along the propagation axis of a focused laser beam. Two different detection types are carried out simultaneously. The "open aperture" and the "closed aperture" Z-scans. The former is based on the measurement of the total laser beam, while the latter on the measurement of the central part of the beam passing through a diaphragm.

Consequently the "open aperture" can give valuable information concerning the nonlinear absorption of a material. On the contrary the "closed aperture" recordings are containing the contributions of the nonlinear refraction and the nonlinear absorption. In this work the nonlinear refraction has been found to be at least one order of magnitude lower than the nonlinear absorption. Consequently the nonlinear optical response is mainly emanating from the nonlinear absorptive part (imaginary part of the third order nonlinear susceptibility Imχ (3) ).

From several "open aperture" Z-scan curves, obtained for different laser energies, the nonlinear optical parameters have been obtained using the procedure detailed elsewhere [START_REF] Sheik-Bahae | Sensitive measurement of optical nonlinearities using a single beam[END_REF][START_REF] Aloukos | Photophysics and transient nonlinear optical response of donor-[60]fullerene hybrids[END_REF]. Briefly the nonlinear absorption parameter (β) has been determined by means of the following equation: (1) where I 0 is the on-axis irradiance at the focus, L eff is the effective thickness of the sample defined as L eff =(1-exp(-α 0 L))/α 0 and α 0 is the linear absorption coefficient of the sample at the laser excitation wavelength. The L eff values used in our data analysis were 9.8 nm and 14.0 nm at 532 nm and 1064 nm respectively.

Then the imaginary part of the third order nonlinear susceptibility has been determined by means of the following equation: [START_REF] Wollhofen | 120 nm resolution and 55 nm structure size in STED-lithography[END_REF] where c is the speed of light in cm s -1 , n 0 is the linear refractive index and ω is the fundamental frequency in cycles per sec.

For the nonlinear optical studies a Nd:YAG laser delivering 11 ns laser pulses at 1064 nm and 532 nm (the latter obtained by frequency doubling), with a 10 Hz repetition rate has been employed. The laser beam has a Gaussian profile, while the beam waist (corresponding at 1/e 2 intensity) has been measured to be 41 μm and 39 μm for the 1064 nm and the 532 nm respectively. During the Z-scan studies, it is of great importance to keep the irradiated area unchanged. In the case of the Sb 2 Te 3 -based thin films studied here, this means that no damage/ deformation of the sample and no modification of the crystallization state shall arise during the measurements. On the contrary low energies do not provide sufficient signal to noise ratios in order to obtain high quality measurements. For this reason special care has been taken in order to assure that the signal to noise ratio has been sufficient, while the transmission of the irradiated area remained unchanged during the measurements.

Results and discussion

Due to the deposition process, the fabricated Sb 2 Te 3 layers are amorphous and enhancing their nonlinearity requires a high degree of crystallization. This is due to the fact that the high saturable absorption efficiency is attributed to a resonant bond weakening with temperature [START_REF] Liu | Nonlinear absorption of Sb-based phase change materials due to the weakening of the resonant bond[END_REF]. More specifically the temperature at the center of the irradiation area is higher due to a higher intensity of the Gaussian laser beam, while it is gradually decreasing towards the edge of the beam. This temperature variation modifies the Sb 2 Te 3 lattice, which in turn alters the resonant bond. Consequently, an initial strengthening of the resonant bond throughout the thin film is necessary, which can be done by aligning the atoms through annealing. This mechanism has been reported to result to a monotonous decrease of the linear absorption coefficient with increasing temperature (dα/dt = -5.89 x 10 3 m -1 K -1 ).

In order to achieve that, firstly, XRD studies radiation have been performed by in-situ annealing of the 200 nm films. For this reason, the temperature has been gradually increased from 20°C up to 350°C with a 10°C step. A 10 min annealing has been carried out at each temperature. The XRD patterns have been recorded for these temperatures and some representative XRD signals are shown in Figure 1 for the strongest peak of the XRD pattern.

The curve corresponding to the as-deposited, amorphous sample is also presented for comparison reasons. A gradual increase of the peaks intensity has been observed between 240°C and 300°C. For temperatures higher than 310°C bubble formation has started to appear in the surface of the samples, deteriorating their quality. The optimal temperature found here for the annealing of the Sb 2 Te 3 films is in very good agreement with previous findings [START_REF] Wang | Characterization of Cr-doped Sb 2 Te 3 films and their application to phasechange memory[END_REF][START_REF] Zhang | Characteristics of Sidoped Sb 2 Te 3 thin films for phase-change random access memory[END_REF].

After the temperature optimization, the rest of the as-deposited samples, prepared for the nonlinear optical measurements, have been annealed in an oven. The thin films have been heated at 300°C for 24 hours. A long annealing duration has been chosen in order to assure that overall crystallization has been achieved. After the annealing, additional XRD studies have been performed for the annealed and the as-deposited thin films (Figure 2). The asdeposited films present no diffraction peaks. On the contrary, the XRD pattern for the annealed sample corresponds very well to a Sb 2 Te 3 rhombohedral, crystalline structure. The (00l) planes are preferentially oriented parallel to the surface in accordance with previous results [START_REF] Wang | Characterization of Cr-doped Sb 2 Te 3 films and their application to phasechange memory[END_REF][START_REF] Yin | Characterization of nitrogen-doped Sb 2 Te 3 films and their application to phase-change memory[END_REF]18]. The peak appearing at 22.9 degrees is attributed either to an hexagonal Te structure [19] or to a weak presence of TeO 2 in the thin film layer [START_REF] Lv | Preparation and Characterization of Sb 2 Te 3 Thin Films by Coevaporation[END_REF].

Then, Vis-NIR spectrophotometric studies have been carried out. In particular, the transmission and the reflection have been recorded before and after the annealing for the 24 nm-thick silica protected Sb 2 Te 3 thin films. Representative curves can be seen in the figure 3. The annealing resulted to a high increase of the reflectivity and a decrease of the transmission. It has to be noted that the Sb 2 Te 3 bandgap has been reported to be 0.14-0.20 eV, which is far from the laser excitation wavelengths employed for the NLO measurements in this work [START_REF] Park | Optical properties of pseudobinary GeTe, Ge 2 Sb 2 Te 5 , GeSb 2 Te 4 , GeSb 4 Te 7 , and Sb 2 Te 3 from ellipsometry and density functional theory[END_REF][START_REF] Olson | Optical properties of amorphous GeTe, Sb 2 Te 3 , and Ge 2 Sb 2 Te 5 : The role of oxygen[END_REF].

In order to determine the refractive index of Sb 2 Te 3 , we applied a global optimization procedure in the [400-1800nm] range using a single oscillator Drude Modified Forouhi-Bloomer model. It is one of the optical dispersion models which derives from the Kramers-Kronig integration and it includes several 'physical' parameters like the optical bandgap. 8 variable parameters describing the complex refractive index dispersion are optimized to minimize a cost function defined as the standard deviation between calculated and experimental transmitted data. The optimization procedure is described in detail elsewhere [START_REF] Gao | Comparison of different dispersion models for single layer optical thin film index determination[END_REF], and the real part of the refractive index as a function of the wavelength, is shown in Figure 4. This significant modification of the optical parameters of the Sb 2 Te 3 thin films shows the importance of the material for photoinscription.

Then the nonlinear optical response of the thin films has been investigated by means of the Z-scan technique. The nonlinear refraction has been found to be negligible compared with the nonlinear absorption under the same experimental conditions, as mentioned in the experimental part. Representative "open aperture" curves can be seen in Figures 5a and5b obtained at 1064 nm and 532 nm respectively for the 24 nm thickness, annealed films. In the case of the 1064 nm irradiation the incident laser energy per pulse has been 200 nJ, corresponding to a peak intensity of 0.68 MW/cm 2 . In the case of the curve obtained at 532 nm the incident laser energy per pulse employed was 180 nJ, which resulted to the same peak intensity (due to the slightly different size of the beam waists for the two different wavelengths). The transmission maximum of the "open aperture curves" at the focal plane indicates a saturable absorption character at both wavelengths. It shall be noted that no nonlinearity has been detected in the case of the as-deposited thin films. A plethora of experimental curves at different incident laser energies have been fitted and analyzed following the procedure detailed in the experimental section. In this way the nonlinear absorption parameter (β) and the imaginary part of the third order nonlinear susceptibility (Imχ (3) ) have been determined and are shown in Table 1 for the two different wavelengths. An increase of the values can be seen in the case of the 532 nm irradiation. This can be attributed to the higher linear absorption of the sample at 532 nm. More specifically, the linear absorption coefficients of the samples have been found to be 0.09 nm -1 and 0.05 nm -1 at 532 nm and 1064 nm respectively, based on the spectroscopic data shown in Figure 3. Indeed, as previously mentioned, the nonlinear optical response of the Sb 2 Te 3 material under ns laser pulse irradiation is of thermal origin, which can explain the different attributes obtained at the two excitation wavelengths. It has to be noted that the strong nonlinear absorption found here and the multiple beam interference that can arise in the layers can have an impact on the determined nonlinear optical values [START_REF] Wei | A Z-scan model for optical nonlinear nanometric films[END_REF][START_REF] Mirza | Mechanism of large optical nonlinearity in gold nanoparticle films[END_REF]. These aspects are currently studied by our group for the Sb 2 Te 3 silica protected thin film structures.

The knowledge of the NLO response at the NIR part of the spectrum and a direct comparison of the nonlinearity in the visible and the NIR are of great importance and have been until now, to the best of our knowledge, unexplored. It reveals that although in the NIR the nonlinearity decreases by a factor of 2, the nonlinear optical parameters remain significantly high. This is valuable in terms of Super-Resolution applications. Indeed, many chalcogenide glasses and other materials are mainly transparent in the NIR, so multilayers of different materials, including the Sb 2 Te 3 can be designed, exhibiting relatively low losses, which is much more difficult in the visible part of the spectrum. Another advantage of employing an IR excitation is that the super resolved inscriptions can be combined with simultaneous detection of the optical nonlinearities of the materials (as for example the second and the third harmonic generation). The latter cannot be carried out easily using visible irradiation, as the nonlinear optical signals are generated at the UV part of the spectrum, which is highly absorbed by many materials.

The nonlinear optical response of the Sb 2 Te 3 material has not been sufficiently studied in the past. Liu et al have reported a nonlinear absorption value β=-6.63x10 -2 m/W [START_REF] Liu | Origin of the giant optical nonlinearity of Sb 2 Te 3 phase change materials[END_REF]. This value is higher than the values reported in our work. The difference between the obtained values is due to the fact that Liu et al employed 50 ns duration laser pulses at 632.8 nm (by modulating a He-Ne laser). This difference of the pulse durations (by a factor of 5) can give rise to the one order of magnitude difference between the determined parameters. Indeed it has been previously found [START_REF] Liu | Nonlinear absorption of Sb-based phase change materials due to the weakening of the resonant bond[END_REF] that increasing the pulse duration from 50 ns to 120 ns resulted to a 5-fold increase of the nonlinear absorption, which perfectly explains this discrepancy. In a work by Simpson et al [START_REF] Simpson | Nonmelting super-resolution near-field apertures in Sb-Te alloys[END_REF] it has been found that Sb-Te thin films do not instantly respond to the incident laser light and that a time duration of approximately 10 ns is required. The 11 ns pulse duration employed here allows an efficient activation of the third order nonlinearities within a single laser pulse. This means that excessive heating of the irradiated area, which can result to a faster damaging of the samples, is avoided.

The most important parameter, which shows the possibility to employ a material for super-resolved inscription/storage is the transmittance maximum of the normalized "open aperture" Z-scan curves (see Figure 3). In our work a value of 1.06-1.07 has been obtained, while a similar value has been reported by Liu et al (approximately 1.10) [START_REF] Liu | Origin of the giant optical nonlinearity of Sb 2 Te 3 phase change materials[END_REF]. In another work by the same group, carried out using 100 ns duration pulses at 405 nm [START_REF] Wei | Nano-optical information storage induced by the nonlinear saturable absorption effect[END_REF], a 1.10 transmittance maximum has been found. Ma et al [START_REF] Ma | Nanoscale lithography with visible light: optical nonlinear saturable absorption effect induced nanobump pattern structures[END_REF] have shown that a Si nonlinear mask can form approximatively 80 nm nanostructures in an AgInSbTe thin film, having a transmittance maximum of about 1.010, much lower than the values reported here. The possibility to use the saturable absorption for local modification of the linear and nonlinear optical properties of materials in order to fabricate optical devices in the nanoscale has not been yet demonstrated. Our current research is focusing in optimising the NLO response of thin film multilayers towards this direction.

Conclusions

In this work we have optimised the crystallisation state of thin Sb 2 Te 3 films in terms of their third order nonlinear optical response. The crystallisation has been confirmed by means of XRD measurements. The nonlinear optical response has been studied by means of the Zscan technique, using nanosecond laser pulses at the visible and the NIR parts of the spectrum. In all cases high nonlinear absorption parameters have been found (of the order of 10 -3 m/W). The prepared samples can be very promising for photonic applications related with photoinscription of nano-photonic components.

Figure Captions:Fig. 1 :

 1 Figure Captions:

Fig. 2 :

 2 Fig. 2: XRD pattern of an annealed (300°C) and an as-deposited sample.

Fig. 3 :

 3 Fig.3: Transmission and reflectivity spectroscopic measurements before and after the annealing of the thin layers.

Fig. 4 :

 4 Fig.4: Refractive index of the Sb 2 Te 3 thin films as a function of the wavelength, obtained by a modified Forouhi-Bloomer model.

Fig. 5 :

 5 Fig. 5: "Open aperture" Z-scans recorded at (a) 11 ns, 1064 nm, 200 nJ and at (b) 11 ns, 532 nm, 180 nJ for the Sb 2 Te 3 annealed thin films.

Acknowledgements

This work was supported by the Region PACA (Project: APEX 2017 NANOFAB)


Maria Grazia Melis

Marie Elise Porqueddu

NEW DOCUMENTATION ON DIGGING TECHNIQUES OF THE PREHISTORIC FUNERARY HYPOGEA OF THE WESTERN MEDITERRANEAN

Keywords: Rock-cut tombs, digging techniques, experimental archaeology, photogrammetry P AROLE CHIAVE -Ipogei funerari, tecniche di escavazione, fotogrammetria

A BSTRACT -The digging of rock-cut tombs in Sardinia underwent an important development during the 4 th millennium BC, in particular in the north-western part of the island.The subject is currently being re-examined by Maria Grazia Melis and her team through field research at S'Elighe Entosu. This necropolis is composed of eight hypogea, dug between the Final Neolithic and the Bronze Age. The study deals with various themes, including the positioning of the necropolis within the landscape, the architecture of the tombs and the diverse phases of related human activity. Recently the architectural data has been updated through the study of excavation techniques employed in creating the monuments. The new information has been fundamental in understanding the articulation of human frequentation of the site and the history of the various modifications made to the hypogea. The investigation was based on the analysis of excavation or tool marks present on the surfaces of the cuts and on the analysis of tools found in Tomb IV. Experimental archaeology played an important role in the proceedings. This research has led to the creation of a database of tool-marks, the study of picks and the experimental reproduction of this type of instrument.

INTRODUCTION

In the western basin of the Mediterranean the phenomenon of rock-cut tombs has its earliest manifestations in Sardinia in the first half of the 5 th Millenni-um cal. BC. The practise underwent an important development during the 4 th millennium in the ambit of the Ozieri facies, and in particular in the north-western part of the island [START_REF] Meloni | Entità, diffusione e aspetti dell'ipogeismo funerario nella Sardegna settentrionale e centro-orien-tale[END_REF]. The hypogea of this period are given the Sar-dinian name of domus de janas; there are more than 3000 known examples, of which roughly 1350 are in the province of Sassari.

In 1994 a congress was held in Sardinia [START_REF] Melis | I-II. -2010 -Usini. Ricostruire il passato. Una ricer-ca internazionale a S'Elighe Entosu[END_REF], which represented an important opportunity for the international scientific community to meet and exchange ideas. Roughly twenty years later a project has been initiated that involves Italy, France and Spain, aimed at promoting the debate on the general themes of prehistoric hypogea of the western Mediterranean, with particular attention to insular contexts and to the ways in which they were initially created.

At the heart of the Italian participation in the project is the study of the necropolis of S'Elighe Entosu (Usini, Sassari), in north-western Sardinia (figs. 1-2). It was formed of nine hypogea, one of which was of uncertain identification, one was dug in the Middle Bronze Age and the remainder date to the Final Neolithic. It became part of a multi-year research programme, under the direction of the author (Melis 2010;Melis et alii 2011), aimed at a reconstruction of the relationship between the necropolis and the surrounding territory. Currently architectonic characteristics and the various phases of excavation of the underground chambers are being examined in greater detail. This is done through morphological/technological analyses of the digging marks visible on the surfaces of the tombs and a technological and functional analysis of the tools used to dig the hypogea. Subsequently experimental activity is added to the research, providing important data to help verify technological considerations. The basis of the experimentation was provided by the technological and functional examination of the picks discovered in tomb IV of S'Elighe Entosu. Almost all of these digging instruments were found in the Bronze Age occupation layers of the corridor of the tomb, reused as building material for a succession of cobbled floor surfaces.

The study of digging methods is particularly important because notwithstanding the large number of this type of tomb present on the island, the subject has only occasionally been examined [START_REF] Tanda | Arte e Religione della Sardeg-na preistorica nella necropoli di Sos Furrighesos-Anela[END_REF][START_REF] Melosu B | -Gli strumenti da scavo del-la tomba VII di Montessu (Villaperuccio-Cagliari): proposta di classificazione tipo-logica[END_REF]; this is also the case in internationally, where discussion of the topic remains to a certain extent undeveloped.

The necropolis of S'Elighe Entosu constitutes an important archive because these monuments underwent diverse phases of architectonic adjustment; these modifications are very often most clearly seen through the various marks left on wall surfaces, the result of using different techniques and tools. Most recently attention has been focused in particular on tombs III and IV. Domus III still contained some traces of the most ancient phase of excavation on the walls of its entrance corridor; the antechamber underwent two phases of enlargement, both through the use of metal tools. Tomb IV is distinguished by its extremely long dromos, which due to its exceptional dimensions represents an extremely important element in the architecture of hypogea. The corridor, notwithstanding its poor state of conservation, still bears marks created during the initial digging of the tomb in part of the south-west wall.

In order to reliably date the marks it will be necessary to extend the research to those features with a well defined chronology; for example domus VII, which, unlike the others, was dug during the Middle Bronze Age, and the tombs from the The reading of these marks is often difficult and is sometimes complicated by both human activity over time (changes to the shape of the tomb, wilful damage etc), and by erosion and natural decay of the rock. It must also be remembered that the most ancient phases, corresponding to the digging of the hypogea during the Final Neolithic, are generally noted for the fine finishing of their surfaces; this procedure obviously obliterates marks made during the preceding passages of the chaîne opératoire, leaving only the final stage evident. This is mostly seen in the inner chambers, while in the various dromos it appears that this phase of finishing was not undertaken, as digging marks left by stone tools are still visible.

The study of digging techniques of the hypogea was entrusted in 2012 to Marie Elise Porqueddu within the remit of the mémoires de Master 1 and 2 at the Université de Bourgogne (Porqueddu 2011(Porqueddu -2012;;[START_REF] Fiorini A | Tablet pc, fotogrammetria e pdf 3D: strumenti per documentare l'archeologia[END_REF]-2013). Currently the subject is the basis of her doctorate thesis run concurrently with two universities (Aix-Marseille Université -Università di Sassari), in which the discussion is approached over a broader territorial scale; the study is in fact extended to include hypogea in France, and in particular those of Fontvieille in the Departement of Bouches du Rhône (southern France).

The experimental activity was undertaken by LaPArS (Laboratorio di Preistoria e Archeologia Sperimentale), also utilising students from the Università di Sassari. Through this experimentation, a new approach to the study of hypogea is possible, though it also provides new perspectives and insights into the organisation of the human groups at S'Elighe Entosu; among the results there should be information on the times, methods, technical knowhow and organisation of the people involved.

DOCUMENTATION OF EXCAVATION MARKS

The study of digging marks on the walls of funerary hypogea has raised the question of their documentation, which shares some of the aspects of recording rock art. The documentation methods in this field have evolved over time to provide results of ever greater definition, while using noninvasive methods to safeguard the surfaces under examination.

In the past the recording of rock art in Sardinia was documented through systems requiring physical contact (Tanda 1994: 14); more recently, in the same area of Usini, oblique light photography has been used, taken from a fixed point using illumination to highlight surfaces from various angles [START_REF] Cassen | -Recording Art on Neolithic Stelae and Passage Tombs from Digital Photographs[END_REF][START_REF]L'arte parietale dell'ipogeo di Chercos[END_REF]. This method holds several advantages, among them the precision of the documentation and the reduction of time spent in the field. It also allows the creation of a unified image of an elaborate picture, permitting a general overview of a figurative composition. Nevertheless, the resulting product remains a two-dimensional document, and its usefulness is limited for the study of technological aspects, which require a three-dimensional image. Three-dimensional restitution is, in fact, indispensable for the study of the morphology of the incisions, for the identification of the tools used and for the reconstruction of the methods employed by the engraver.

Similar limitations apply to Digital Image Enhancement software such as DStretch plug-in for ImageJ (Defrasne 2014), that nonetheless constitute a useful instrument for identifying and evidencing faint or difficult to see images.

The adoption of a specific method of documentation must necessarily depend on factors including the type of subject to be analysed, on the level of illumination, the state of conservation and of the objectives of the documentation. A useful solution is to combine both 2D and 3D techniques (Cassen et alii 2014;Domingo et alii 2013). Recently the integration of RTI (Reflectance Transformation Imaging) and 3D Laser Scanning has been used to study the steles of the Iberian Late Bronze Age, with the advantage of each compensating for the limitations of both methodological approaches (Diaz-Guardamino, Wheatley 2013). Other 3D recording techniques have been used in the documentation of rock art in the Alpine region, including SLS (Structured Light Scanning) and SfM (Structure from Motion) (Marretta 2014).

A two-dimensional document was initially made to record the excavation marks on the walls of the S'Elighe Entosu hypogea, using the oblique light method, which gave interesting early results. That was then later integrated with a 3D image. To this end we are currently testing the use of photogrammetry together with a 3D Laser Scanner, an approach also used to create aerial documentation of large outdoor areas, which in the context of the S'Elighe Entosu project has been used for the UAV (Unmanned Aerial Vehicle) survey of sever-al archaeological sites (Melis et alii 2013;Melis with Oben s.r.l., ongoing research).

Photogrammetry and 3D Laser Scanning, which have both been at the centre of a lengthy debate (see, for example, Baltsavias 1999; [START_REF] Böhler | -3D scanning and photogrammetry for heritage recording: a comparison[END_REF]Ferreira et alii 2014;Grussenmeyer et alii 2008;[START_REF] Et Université De Paris X Nanterre | -Combining 3D Laser-Scanning and Close-Range Photogrammetry -An Approach to Exploit the Strengths of both Methods[END_REF], are used in various fields, such as for monitoring landscape deterioration, the documentation of rock art and for monitoring incised or engraved surfaces [START_REF] Doehne | An Overview of Current Research[END_REF][START_REF] Moreno | -Low-Cost Photogrammetry and 3D Scan-ning: the Documentation of Palaeolithic Parietal Art in El Niño Cave, in Archaeolo-gy in the Digital Era[END_REF], the survey of archaeological areas and monuments as well as the doc- umentation of archaeological excavations (Girardi et alii 2007;[START_REF] Fiorini A | Tablet pc, fotogrammetria e pdf 3D: strumenti per documentare l'archeologia[END_REF].

At S'Elighe Entosu the first tests were carried out on the north-east and southwest walls of the corridor of tomb III (figs. 2-3), in which part of the original cut remained together with the initial digging marks. The photogrammetry was carried out with a photographic record later processed through Agisoft Photoscan software. The 3D record was realised with a laser scanner Creaform REVscan TM , with a resolution of 0,2 mm.

One of the advantages of laser scanning is the possibility of recording poorly illuminated or unlit surfaces, as well as the immediate acquisition of a three-dimensional document; the disadvantages include the high cost of the technology and the complexity of the field equipment; this includes the laser scanner itself, its power source, a computer and a work surface. The advantages of photogrammetry include lower costs, faster acquisition of data in the field and the relative simplicity of the equipment: a camera and a tripod, sometimes augmented by artificial lighting. However, good illumination of the surfaces to be documented is a necessity, and the data collected in the field must be subsequently processed in order to map the points that will be used to create the three-dimensional model. Neither method is particularly adapted for the documentation of large areas, due to the enormous quantity of data created. Furthermore they can give disappointing results for the documentation of poorly defined marks. Therefore, depending on requirements and objectives it is often necessary to work with a combination of various methodologies (Bueno Ramirez et alii 2014).

m.g.m.

A NEW METHODOLOGY FOR STUDYING THE DIGGING PROCESS

In order to find answers to the problem facing us, a new methodology was drawn up which integrates different techniques and other issues. It was studied and elaborated during a Master thesis. There are three lines of reflection, from the technological and functional analysis of the macro-tools to the study of the marks made by the digging process which are present on the walls of the monuments. Both are connected with the experimental approach which is the final aspect. These main lines of research are complementary and inseparable for the pursuance of the study. The idea of this methodology was born from a consideration ensuing from the poor level of conservation of the necropolis at S'Elighe Entosu.

Indeed, we only have partial data and it is necessary to look at each and every issue in order to reconstruct the operational sequence of the first digging phase of the hypogea.

The first part of the project is the study of the tools. It is based on a technological and functional study directly inspired by and modified from the methodology "Lecture d'un objet lithique taillé" (Inizan et alii 1995).

Due to the nature of the artefacts, the methodology involved needs to be modified on specific points such as a separate phase for the digging marks, for instance. The objective was to reconstruct the complete operational sequence, which includes activity and the use of tools, implicated in the making of the macro-tools. From these analyses, it is also possible to gather data about how they were used, and what techniques were employed in the digging and what order they were used in.

The second objective is the study of the tool marks. Most of them can be easily seen and documented in the tombs of the S'Elighe Entosu necropolis. They are evidence of the use of the tools and techniques on rock. It was particularly difficult to create a methodology to examine these traces because they were not perfectly preserved. The techniques chosen for the study do not require direct contact with the stone surfaces but at the same time they need to guarantee the most faithful reproduction of the marks, in order for the study to be valid. Techniques related to photography and new technology are being applied at S'Elighe Entosu to resolve this problem. Other objectives include the chronological reconstruction of the different phases of digging.

Experimentation is the third aspect of our research and it is used to connect the two other facets of the methodology. The use of experimental archaeology is very important because it made it possible to fill in the blanks left by the other analysis. It helps in understanding the relationship between the tools and the marks. More importantly, the use of experimentation helps in answering anthropological questions regarding the prehistoric human group. It helped in understanding the necessary skills, how the rock-cut tombs were dug and how the process was organised. The experimentation is structured over two phases from the making of tools followed by their use.

DIFFERENT TYPES OF TRACES RELATING TO THE DIGGING PROCESS AT S'ELIGHE ENTOSU

Different kinds of marks are present in the tombs at S'Elighe Entosu. The use of oblique light photography made it possible to highlight them. The different types defined different digging periods. Tombs III and IV are the most relevant examples. The photographic method employed was inspired by the system created and used by Guillaume Robin [START_REF] Cassen | -Recording Art on Neolithic Stelae and Passage Tombs from Digital Photographs[END_REF][START_REF]L'arte parietale dell'ipogeo di Chercos[END_REF].

The three different types of marks are present in tomb III. Most of them are located in the antechamber and in the corridor leading to the principal chamber. They demonstrate two phases of digging. The first one is the lower part of the antechamber which is interpreted as a phase of floor preparation. There are linear and regular marks, possibly made by a metal tool. That phase is also distinguished by the creation of a separate space in one corner. The second type corresponds to marks mainly present on the roof and the higher section of the antechamber and the corridor. There are many marks made by a rectangular metal tool, and they are more recent. In the corridor, the contrast between the higher and lower part of the area is important. Initially, the area was rectangular with straight walls and clearly defined angles. These two types of marks support the results of finds analysis from this tomb and prove that it was reused in different periods (fig. 4). No experimental study related to these marks was carried out.

Tombs III and IV each possess a very long corridor that gives access to the antechamber. These corridors display the third type of mark. Circular in form, they are very different from the others. They are typical of the use of a tool similar to a pick. The marks from tomb III were documented by photogrammetry and 3D laser-scanning (figs. 2-3). We obtained a more faithful virtual model of digging- marks in order to better study them. This is particularly important because the traces were not well preserved due to their position in the corridor. Indeed, the marks in the corridor are exposed to the weather and to light.

Similar traces are present in the corridor of tomb IV. They are particularly evident at the end of the passage where the conditions are favourable for their conservation. They are present on both the floor and the walls and made it possible to identify the end of this long corridor.

Based on the observation of this last group, the fact that it is really different from the other two and the discovery of tools in tomb IV, we started to hypothesise that those traces were due to the impact of that particular tool. It means that this type of mark is related to the first phase of the digging of the tombs during the Neolithic.

This preliminary study of the marks gave the first information about them and furthered better understanding of the different phases of the monuments. It provided important chronological data regarding how, after the Neolithic period, these tombs were reused during Roman, Medieval and post-Medieval times. This different approach to the structures made it possible to further the analysis and to look at problems of conservation.

THE DIGGING TOOLS: DIFFERENT MOR-PHOLOGY FOR DIFFERENT FUNCTIONS?

Seven tools were found at S'Elighe Entosu. They were discovered during different excavations, coming from tomb IV and its surroundings. All of the tools are picks. There were examined through a technological and functional analysis as part of a Masters thesis. The objective is now to continue the study through experimentation and comparison with other types of material, for example the tools from another necropolis, at Santu Pedru, also located in northeast Sardinia. The PhD project included the study of the French necropolis at Fontvieille where the same methodology is applied.

The first result of the analysis was to divide the tools into three groups. These groups were based on criteria such as shape but also on the presence of use-wear usewear traces and stigmata created during manufacture and the type of raw material used. The first group is composed of three instruments, tools number 2, 4 and 7 (figs. 5-6).

These tools are of a similar shape, roughly the same size and made from the same raw material. Indeed, there are made from andesite, although which specific type is still to be defined. They possess a sub-quadrangular middle section and two straight faces, A and D. The other faces, B and C, underwent a good deal of work, implying the need to create a regular surface and forming the convex outer edge. Some of the marks observed on this part, face E, are evidence of the use of these tools. All seven tools were at some point employed. In this group the tools are of modest dimensions, i.e. between 12 and 14 centimetres long, 6 and 8 centimetres wide. Tools number 4 and 7 are also the lightest weighing 716 and 630 grams.

Tools number 1 and 6 are of larger dimensions and form a second group (figs. 7-8). They are longer than those of the other groups. In fact tool number 1 is the longest of the group with a length of 22,5centimetres, a width of 7,7 cen-n. 2 n. 4 n. 7 same marks due to its poor conservation. Tool 1 was made from limestone while tool 6 was made of andesite.

The last group is composed of instruments number 3 and 5 (figs. 9-10). They were not found intact, with only the functional part surviving. They are distinguished by the presence of a peak and a straight fracture on face F. There are different theories for why this is so. The first of these is based on the premise that in other contexts in Prehistory, materials were found broken in order to remove their significance and render them useless before being abandoned. It is a theory related to the importance of these tools and may hold some ritual significance. There are other similar contexts in Sardinia such as Anghelu Ruju and Iloi Ispiluncas (Cappai, [START_REF] Cappai R | -Signe et fonction des objets lithiques préhistoriques en Sardaigne, Les données de la nécropole d'Ispiluncas -Sedilo (Sardegna-Italia)[END_REF]. As far as S'Elighe Entosu is concerned, this possibility remains uncertain for the moment as we cannot be sure that the picks were found in a primary deposit. This consideration leads us to the second hypothesis which is related to the stratigraphic position of the tools. Indeed, they were found in a context dated to Middle Bronze Age, n. 3 n. 5 adding another phase to the use of tomb IV. This context was formed of a bed of calcareous stones creating a floor surface. It is probably due to this that the tools were broken before being included in the layer. Difficulties surrounding the conservation of the stratigraphy makes it harder to be certain of this and therefore support the hypothesis. It is to be hoped that comparison with finds from other sites will help shed light on this.

The poor state of conservation of the tools and of the context are a limit to the technological analysis but the preliminary data made it possible to identify some similarities and differences between the tools. From this data it is possible to begin to hypothesise about the various phases of the operational sequence.

Indeed, the choice of raw materials used for the tools and the lack of finesse in their making makes one think that the work sequence was opportunistic. This was evident from the lack of technical investment, the skill and the time taken during the operational sequence to make the tools. The raw materials used are to be found near the necropolis, in the bed of the river Riu Mannu. They are probably river pebbles. Concerning the shaping step in the sequence, two phases were recognised, one for the creation of the pre-form and one for the specifics of the finished object. For some tools, it is also possible that there was only one phase of the sequence. The choice of the stone is probably based on the form of the raw material and on its quality which make the creation of the instrument quicker. The same technique is used for the second step, consisting of a hammering technique characterised by a direct blow using a hard hammer. This is a basic and simple technique and it is clearly visible on tool number 1 (fig. 6, details 2 and 6).

These results should lead to further considerations, mostly concerning shafts or handles. The work is still to be developed on this aspect but also on the fact that we have different groups of tools. Are they used in the same way and during the same phase of work ? We need to work on their function more precisely.

A PROTOCOL FOR EXPERIMENTATION: FROM TOOLS TO DIGGING MARKS

We can begin to answer the questions facing us through experimentation. The experimental protocol is divided into two parts; production of the tools themselves and the subsequent use of them on stone in order to create experimental marks. The first stage was realised during the Masters course in 2013, at the LaPArS, at Sassari University. It was performed by a group of students of the University as a didactic activity.

The students participated in activities searching for the raw materials that could be used to make these tools. This was concentrated in the area surrounding the necropolis and in the bed of the Riu Mannu river in the search for calcareous stones and river pebbles. The process also involved the use of geological maps to identify areas where andesite could be found. Two sites were identified, both between 12 and 15 kilometres from the necropolis. One of them is directly connected with the Riu Mannu and the research also included a survey of that area. This confirmed theories about the use of river pebbles for making picks. Different types of stone were collected, one type for the tools and another for use as hammers. These were in trachyte, andesite and basalt. We did not find andesite river peb-bles with the pre-form that we required for the tools. Because of this, it was decided to exclusively employ limestone.

The next stage was the realisation of the tools. Different techniques were tested for the shaping of the instruments but the foremost was direct and indirect blows with a hammer (fig. 11). The protocol involved the use of different hammers of various weight and form. This choice depended on the rock to worked on and on the phase of the operational sequence. All the experimental work was carried out on a stone floor. Many attempts were necessary to obtain useful results, the use of six tools was attempted but only two examples were satisfactory. Indeed, a few problems arose during the experimentation. Being the first time that we attempted to make experimental tools for digging some errors were made. The first mistake appeared at the beginning of the operational sequence. An error was made during the choice of the raw materials for the picks. They didn't all have the necessary quality to withstand the different techniques. On top of that, during the test other mistakes were made that did not provide solutions. These mistakes helped in the improved understanding of the operational sequence and the techniques employed, greatly adding to our knowledge.

This first step of the experimental protocol showed that the tools were created with simple technique and demonstrated that it was not necessary to have specialist knowhow. The principal technique was the use of direct blows, which is a simple method and included the variation of hammering styles. This technique was used for preparing part of the object in order to make a handle for the tools (fig. 12). We noticed that the knowledge re- quired for the choice of the raw materials to be used in making the tools was more important than the level of skill for the techniques employed. This choice may well be the most important part of the operational sequence. The successful manufacturing of tools depends on it because a better initial choice limited potential mistakes and lowered the time involved during the following operations of the sequence.

The second step of our experimental protocol is planned for 2016, once again with the participation of a group of students. The program included the use of 15 to 20 tools with different weights and dimensions and different types of haft. The goal is to use as many tools as possible in order to avoid any mistakes or misunderstandings during the work but more importantly to answer our questions. In this next stage, we will test the variability of tools with different dimensions and see in which ways they can be used. The variability of techniques can also show how each of the tools can be used, what technique is the most effective and in which circumstances they can be used. The principal objective is still to connect tools and marks. Performing the second stage experimental marks will appear. The objective is to study them and make com-parisons with the archaeological evidence.

The realisation of this experimental programme is of real interest even though it is of limited size, confronting various problems. It helps in the comprehension of the operational sequence regarding the picks and answers many of our questions.

m.e.p.

FINAL CONSIDERATIONS AND OUTLOOK FOR FUTURE RESEARCH

In recent years the study of digging methods of rock cut tombs has undergone an important development with the introduction of a methodology that integrates morphological-technological analysis with experimental archaeology. This approach was applied to the domus de janas of S'Elighe Entosu, that contain evidence of diverse phases of excavation, identified through the examination of digging marks on the walls.

The research has shown that the areas best suited to the study of these marks were the corridors, in which there was no final phase of finishing and the traces of excavation, where they survived, were easily visible. The inner rooms show various periods in which modifications were made to the earliest phase of excavation, which were identifiable through marks of a different type, made by differing tools.

The study was organised in four main phases; a morphological-technological study of the digging marks, a technological and functional study of the picks discovered in the necropolis, experimental reproduction of tools and the experimental reproduction of digging marks.

With regard to the fourth phase and the tools themselves a new experimental protocol will be introduced, which will look at studying various forms of handles. Through this protocol a corpus of experimental marks will be created, which will become a databank to be used as reference for comparison with other contents.

At the same time the documentation of excavation marks will continue with the development of 2D and 3D integrated systems of recording.

The elaborated data will necessarily have to be compared to other evidence of marks and the use of tools on a wider scale in Sardinia.

The application of the same methodologies to the context in Fontvieille, France, will represent an important opportunity for comparison of the phenomenon in the Mediterranean area.

Lastly, from the point of view of methodology and the technical means employed, the application of new approaches, underused or so far untried in Sardinia, such as experimental archaeology and integrated 2D-3D documentation of digging marks, will make a considerable contribution to the study of funerary hypogea.

The research is still ongoing, as are both the study and the excavation of the necropolis and the investigation of settlement contexts. In particular the settlements, identified through the presence of surface material, are being examined using an infrared thermal imaging camera, which may provide useful information for an estimate of the demographics of the communities that used thehypogea.

Beyond the chronological distinctions of the various excavation phases of the hypogea, this study, and especially the experimental process, should provide indications as to how the members of the human group were involved in the excavation of the hypogea, on the number of people employed, on the necessary workload and the time required, and therefore on the ramifications that this activity would have exerted on the social and economic organisation of the community. The impact of these results will be of considerable interest beyond the specific case of S'Elighe Entosu, considering the importance of the phenomenon of funerary hypogea in Sardinia and further afield.

Fig. 2 -

 2 Fig. 2 -S'Elighe Entosu (Usini, Sassari). Map of tomb III and localisation of surface documented through photogrammetry and laser scanning. (by Melis 2010; photos M. G. Melis).

Fig. 3 -

 3 Fig. 3 -S'Elighe Entosu (Usini, Sassari). Documented surface of south-west (A) and north-east (B) corridor walls: 3D model obtained by photogrammetry, represented as texture (1) and mesh illuminated by oblique light(2); 3D model obtained by laser scanning, represented as mesh illuminated by oblique light (3) (elab. C. Caradonna, M. G. Melis and P. Fallavollita).

Fig. 4 -

 4 Fig. 4 -S'Elighe Entosu (Usini, Sassari). Modern digging marks created with a metal tool. 1: marks from tomb III, access corridor of the principal chamber; 2: marks from tomb III, lower part of the antechamber (photos and processing M. E. Porqueddu).

Fig. 5 -

 5 Fig. 5 -S'Elighe Entosu (Usini, Sassari). Digging tools n. 2, 4 and 7: faces A, B, C, D and section (drawings and processing M. E. Porqueddu).

Fig. 6 -

 6 Fig. 6 -S'Elighe Entosu (Usini, Sassari). Digging tool n. 4. 1: face C; 2: face A; 3: face E; 4-5: marks from face A (photos and processing M. E. Porqueddu).

Fig. 7 -

 7 Fig. 7 -S'Elighe Entosu (Usini, Sassari). Digging tools n. 1 and 6: faces A, B, C, D and section (drawings and processing M. E. Porqueddu).

Fig. 9 -

 9 Fig. 9 -S'Elighe Entosu (Usini, Sassari). Digging tools n. 3 and 5: faces A, B, C, D and section (drawings and processing M. E. Porqueddu).

Fig. 10

 10 Fig. 10 -S'Elighe Entosu (Usini, Sassari). Digging tool n. 3. 1: face C; 2: face A; 3: face E; 4: detail from face C; 5: face F (photos and pro-cessing M. E. Porqueddu).

Fig. 11 -

 11 Fig. 11 -Techniques used during the experimentation. 1: direct percussion; 2: indirect percussion (photos and processing M. E. Porqueddu).

Fig. 12 -

 12 Fig. 12 -Experimental digging tool n. 1. 1: Raw material; 2: phase of façonnage; 3: final experimental digging tool; 4: hammering marks and part of the "cortex" of the experimental digging tool (photos and processing M. E. Porqueddu).