Light (anti)nuclei production in Pb-Pb collisions at √sNN = 5.02 TeV

This is a self-archived version of an original article. This version may differ from the original in pagination and typographic details. Author(s): Title: Year: Version: Copyright: Rights: Rights url: Please cite the original version: CC BY 4.0 https://creativecommons.org/licenses/by/4.0/ Light (anti)nuclei production in Pb-Pb collisions at √sNN = 5.02 TeV ©2023 CERN, for the ALICE Collaboration Published version ALICE Collaboration ALICE Collaboration. (2023). Light (anti)nuclei production in Pb-Pb collisions at √sNN = 5.02 TeV. Physical Review C, 107, Article 064904. https://doi.org/10.1103/PhysRevC.107.064904 2023 PHYSICAL REVIEW C 107, 064904 (2023) Light (anti)nuclei production in Pb-Pb collisions at √sNN =5.02 TeV S. Acharya et al.∗ (ALICE Collaboration) (Received 10 February 2023; accepted 16 May 2023; published 8 June 2023) The measurement of the production of deuterons, tritons and 3He and their antiparticles in Pb-Pb collisions at √sNN =5.02 TeV is presented in this article. The measurements are carried out at midrapidity (|y|< 0.5) as a function of collision centrality using the ALICE detector. The pT-integrated yields, the coalescence parameters and the ratios to protons and antiprotons are reported and compared with nucleosynthesis models. The comparison of these results in different collision systems at different center-of-mass collision energies reveals a suppression of nucleus production in small systems. In the Statistical Hadronisation Model framework, this can be explained by a small correlation volume where the baryon number is conserved, as already shown in previous fluctuation analyses. However, a different size of the correlation volume is required to describe the proton yields in the same data sets. The coalescence model can describe this suppression by the fact that the wave functions of the nuclei are large and the fireball size starts to become comparable and even much smaller than the actual nucleus at low multiplicities. DOI: 10.1103/PhysRevC.107.064904 I. INTRODUCTION Collisions of ultrarelativistic heavy ions create suitable conditions for the production of light (anti)nuclei, as a high energy density is reached over a large volume. Under these conditions, hot and dense matter, which contains approximately equal numbers of quarks and antiquarks at midrapidity, is produced for a short duration (a few 10−23 s). After a deconfined quark-gluon plasma (QGP) is formed in the initial state, the system cools down and undergoes a transition to a hadron gas. While the hadronic yields are fixed at the moment when the rate of inelastic collisions becomes negligible (chemical freeze-out), the transverse momentum (pT) distributions continue to change until elastic interactions cease (kinetic freeze-out). The observed nucleus abundance is highly sensitive to the chemical freeze-out conditions as well as the dynamics of the emitting source. The production of light nuclei and antinuclei has already been measured in many experiments at various energies in heavy-ion collisions at the Bevalac [1], the Schwerionensynchrotron (SIS) [2,3], the Alternating Gradient Synchrotron (AGS) [4–8], the Super Proton Synchrotron (SPS) [9–12], the Relativistic Heavy Ion Collider (RHIC) [13–20], and the Large Hadron Collider (LHC) [21–25], and in smaller collision systems [22,26–38]. The production of light nuclei is usually discussed within two theoretical approaches: the nucleon coalescence model [39–44] and the statistical hadronization model (SHM) [45–49]. ∗Full author list given at the end of the article. Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI. Generally, the coalescence model describes the production of nuclei from the nucleons emitted from a hot fireball that cools down while expanding. Most variants use a phasespace picture for the formation; namely the nucleons have to be close in space and (relative) momentum to allow for the formation of the nucleus. In particular, the studies of the production of (anti)nuclei as a function of the chargedparticle multiplicity [22] have clearly shown experimentally a dependence of the yield (ratios) on the volume of the emitting fireball. In fact, a strong suppression of nucleus-to- proton yield ratios is seen from high multiplicities in Pb-Pb to lower multiplicities in p-Pb, and reaching small multiplicities in pp [37,38] collisions. The size of the fireball can be extracted from the measurement of two-particle correlations, of Hanbury Brown–Twiss type [50–52], nowadays often called femtoscopy. Empirically, it was found that the charged-particle multiplicity of the collision is proportional to the size parameter Rcubed [44,53]. Theoretically, these correlations can be directly connected to the coalescence parameter BA, which is a measure for the probability to form a nucleus of mass number Afrom the corresponding nucleons [40–42,44,54–56]. This dependence is mainly given by the fact that the wave functions of the nucleons have to overlap with the nucleus’s wave function, while the constituents are being emitted from a region of homogeneity of the fireball. This leads to a strong suppression of nucleus production in small systems, since the size of the formed nucleus becomes larger than the emitting source [44,57]. It is worthwhile to mention that coalescence models typically ignore the problem of conservation of energy and momentum in the process, assuming either that this is handled via the off-shell nature of the particles or additional particles involved in the process itself. The SHM successfully describes hadron yields in heavyion collisions, in particular in central collisions and at 2469-9985/2023/107(6)/064904(16) 064904-1 ©2023 CERN, for the ALICE Collaboration S. ACHARYA et al. PHYSICAL REVIEW C 107, 064904 (2023) midrapidity [48]. The production of nuclei is solely determined by their quantum numbers and masses [49]. For more peripheral heavy-ion collisions or even smaller collision systems such as pp and p-Pb, one needs to switch from a grand canonical ensemble to a canonical description of the relevant quantum numbers (baryon number B, charge Q, and strangeness S)[58,59]. The canonical ensemble requires a local conservation of each quantum number in a particular volume Vc, the so-called correlation volume. Interestingly, Vccannot be unambiguously determined from first principles [60], but it can be constrained from measurements of the event-by-event number fluctuation of net protons [59,61]or deuterons [25]. Other approaches include a nonequilibrium treatment of the quantum numbers in question (see Ref. [49] and references therein) or even a partial chemical equilibrium (PCE) [62–64]. In this article, the production of deuterons, tritons and 3He and their antiparticles in Pb-Pb collisions at a center-of-mass energy per nucleon pair √sNN =5.02 TeV is reported. The pT-integrated yields, the coalescence parameters (calculated using average of protons and antiprotons, since they are found to be produced in same abundance at the LHC energies [65]) and the ratios to protons and antiprotons are compared with nucleon coalescence and statistical hadronization models. II. EXPERIMENTAL APPARATUS AND DATA SAMPLE The results presented in this article are based on the data set of Pb-Pb collisions at √sNN =5.02 TeV collected in 2018. In total, 230 ×106events were analyzed, of which 86.7×106 are central trigger events in the 0–10% centrality interval and 74.3×106are semicentral trigger events in the 30–50% centrality interval. The ALICE detector [66,67] has excellent particle identification and vertexing capabilities. The (anti)nuclei were measured using the Inner Tracking System (ITS), the Time Projection Chamber (TPC) and the time-of-flight (TOF) detector. All these detectors are located inside a homogeneous magnetic field with a strength of 0.5 T and cover the full azimuthal acceptance and the pseudorapidity range |η|<0.9 for interactions located in |z|<10 cm, where zis the distance from the nominal interaction point along the beam direction. The ITS [68] consists of six cylindrical layers of (positionsensitive) silicon detectors, covering the central rapidity region. The ITS allows the reconstruction of the primary and secondary vertices. It is also used to separate primary nuclei from secondary nuclei via the distance of closest approach (DCA) of the track to the primary vertex with good resolution (better than 300 µm), assured by the Silicon Pixel Detector (SPD), which comprises the innermost two layers of the ITS. The TPC [69] is the main tracking device of the experiment. It is a gas-filled cylinder and provides particle identification via the specific energy loss (dE/dx). (Anti)3He are identified up to pT=7GeV/cusing the TPC only. The TOF detector [70] allows for the light (anti)nuclei identification by means of the velocity determination. Its total time resolution for tracks from Pb-Pb collisions corresponds to about 65 ps which is determined by the intrinsic time resolution of the detector and the resolution of the event collision time measurement. By a combined analysis of TPC and TOF data, (anti)deuterons are identified up to pT=6GeV/cin Pb-Pb collisions. (Anti)tritons are also identified using TPC and TOF. However, due to a sizable background starting at about 2 GeV/coriginating from mismatches between a track and a cluster in TOF, the (anti)tritons can only be measured up to pT=3.2GeV/cin this data set. The Transition Radiation Detector (TRD) [71] was designed to provide electron identification and triggering and to improve the track reconstruction and calibration in the central barrel of ALICE. The TRD improves the overall momentum resolution of the ALICE central barrel by providing additional space points at large radii for tracking, reducing as well significantly the probability of mismatch between tracks and TOF hits for rare probes analyses such as the triton analysis presented in this article. Finally, a pair of forward and backward scintillator hodoscopes (2.8<η<5.1 and −3.7<η<−1.7), the V0 detectors [72], measures the arrival time of particles with a resolution of 1 ns. The V0 detectors are used for triggering purposes and for rejection of beam-gas interactions. Furthermore, it provides the centrality determination in Pb-Pb collisions. III. DATA ANALYSIS A. Event and track selection The data were collected using a minimum-bias trigger requiring at least one hit in both the V0 detectors. In addition, a central and a semicentral trigger were used, also determined by the V0 detectors, selecting collisions in the 0–10% and 30–50% centrality intervals, respectively. Moreover, the timing information of the V0 scintillator arrays is used to reject the events triggered by the interactions of the beam with the residual gas in the LHC vacuum pipe. A further selection using a zero degree calorimeter is applied in order to reject the electromagnetic beam-beam interactions and beam-satellite bunch collisions [73]. These three rejections are done in the offline analysis. The production yield of primary (anti)deuterons, (anti)tritons and (anti)3He are measured at midrapidity. In order to provide optimal particle identification by reducing the difference between transverse and total momentum, the spectra are provided within a rapidity window of |y|<0.5. Only tracks in the full tracking acceptance of |η|<0.8are selected. In order to guarantee good track momentum and dE/dx resolution in the relevant pTranges, the selected tracks are required to have at least 70 out of 159 possible reconstructed points in the TPC and two points in the ITS (out of which at least one is in the SPD). The requirement of at least one point in the two innermost layers, the SPD, assures a resolution better than 300 µm on the distance of closest approach to the primary vertex in the planes perpendicular (DCAxy) and parallel (DCAz) to the beam axis for the selected tracks [67]. Furthermore, it is required that the χ2per TPC reconstructed point is less than 2.5 and tracks of weak-decay 064904-2 LIGHT (ANTI)NUCLEI PRODUCTION IN Pb-Pb … PHYSICAL REVIEW C 107, 064904 (2023) FIG. 1. Specific energy loss of charged tracks in the TPC vs rigidity (p/z) for Pb-Pb collisions at √sNN =5.02 TeV. The dashed lines represent parametrizations of the Bethe-Bloch curve. Particles lighter than deuterons have been removed by applying a selection in the dE/dx vs p/zplane that corresponds to the upper edge (3σ)of the proton band such that only nuclei are visible. products are rejected as they cannot originate from the tracks of primary nuclei. B. Particle identification The TPC allows for a clean identification of (anti)3He in the whole pTrange and of (anti)deuterons up to pT≈ 1GeV/c. For higher transverse momenta, the dE/dx information for charged particles is combined with the TOF mass determination in the (anti)deuteron analysis. For the (anti)tritons in the whole pTrange, a combined TPC and TOF analysis is performed. Figure 1shows the TPC specific energy loss as a function of rigidity (p/z) in Pb-Pb collisions at √sNN =5.02 TeV. The dashed curves represent parametrizations of the Bethe-Bloch formula for the different particle species. The (anti)deuteron and (anti)3He identification with the TPC is achieved by requiring that the energy-loss signal of a track lies in a 3σwindow around the expected value for a given mass hypothesis, where σis the dE/dx resolution. For the (anti)tritons, a reduced 2σwindow is employed in order to further decrease the background. In order to extend the pTreach of the measurement, it is additionally required that the track is matched to a hit in the TOF detector. As shown in Fig. 2, based on the time-of-flight measurement the squared mass of the particle is determined in different pTintervals and the distributions are then fitted using a Gaussian function with an exponential tail for the signal. The background of the (anti)deuterons mainly originates from two components, namely wrong association of a track with a TOF hit and the non-Gaussian tail of lower mass particles. For the (anti)tritons the dominant background originates from the wrong associations of a track with a TOF hit. For both nuclei, the background is described with the sum of two exponential functions. C. Background rejection Among of the main sources of background in the analyses of the primary deuteron and triton production are nuclei originating from secondary interactions. These secondary nuclei come mostly from the interactions of other primary particles with the detector material. In some of these interactions, a light nucleus can be produced by spallation processes, i. e., can be knocked out from detector or from support material. The baryon number conservation sets a very high energy threshold for the production of secondary antinuclei with similar processes, thus making the contribution of secondary antinuclei from material negligible, as also confirmed by simulations. Other processes, such as the decay of (anti)hypernuclei, represent a negligible contamination of the observed (anti)deuterons and (anti)tritons. As already done in previous analyses [21–25], in order to subtract the background from secondary deuterons and 3He the DCAxy is used. The distribution of primary particles is expected to be peaked at DCAxy =0, whereas secondary particles are expected to exhibit a flat DCAxy distributiontothe 1.5−1−0.5−0 0.5 1 1.5 2 2.5 ) 4 c/ 2 (GeV 2 d m - 2 m 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 3 10× ) 4 c/ 2 Counts / (0.6 GeV Data Antideuteron Signal Background Only Total fit = 5.02 TeV NN sPb−5% Pb−0 | < 0.5y, |c < 5.0 GeV/ T p≤4.4 ALICE 2−1.5−1−0.5−0 0.5 1 1.5 2 2.5 ) 4 c/ 2 (GeV 2 t m - 2 m 20 40 60 80 100 120 140 ) 4 c/ 2 Counts / (0.2 GeV Data Antitriton Signal Background Only Total fit = 5.02 TeV NN sPb−10% Pb−0 | < 0.5y, |c < 2.4 GeV/ T p≤2.0 ALICE FIG. 2. Fit to the measured squared mass to extract the antideuteron signal in 4.4<pT<5.0 GeV/c(left) and the antitriton signal in 2.0<pT<2.4 GeV/c(right). The red dashed line shows the background, the solid blue line the combined fit to the data, and the green dashed line the signal only. 064904-3 S. ACHARYA et al. PHYSICAL REVIEW C 107, 064904 (2023) 1−0.5−0 0.5 1 (cm) xy DCA 1 10 2 10 3 10 4 10 5 10 6 10 7 10 8 10 Counts ALICE = 5.02 TeV NN sPb−Pb c < 1.1 GeV/ T p≤1.0 d d 1−0.5−0 0.5 1 (cm) xy DCA 1 10 2 10 3 10 4 10 5 10 6 10 7 10 8 10 Counts | < 0.5y90%, |−0 c < 1.6 GeV/ T p≤1.2 He 3 He 3 FIG. 3. DCAxy of deuterons (open red circles) and antideuterons (solid red circles) for the pTintervals 1.0⩽pT<1.1 GeV/c(left) and of 3He (open blue squares) and 3He (solid blue squares) for 1.2⩽pT<1.6 GeV/c(right). first order. The typical distributions of DCAxy for nuclei and antinuclei detected in ALICE are shown in Fig. 3. In second order, the tracks originating from secondary particles may be associated to a wrong hit in the innermost layers of the ITS. If the latter belongs to a primary particle, the extrapolation of the secondary particle track will wrongly point to the primary vertex, as the track pointing is mostly driven by the hits in the innermost layers of the ITS. In the deuteron and 3He analyses presented in this article, a fit to the observed DCAxy distribution is performed to extract the primary fraction of deuterons and 3He. The DCAxy distributions of primary and secondary deuterons as well as 3He in each transverse momentum interval are extracted from Monte Carlo (MC) events and are used as templates to fit the measured DCAxy distribution. Since the secondary particles have large DCAxy, the fits are done in a range of DCAxy wider than the actual track selection criterion to better constrain the secondary particle components. The contamination from deuterons produced in the interactions with the detector material is only significant below 1.4 GeV/c. In contrast to deuterons, the background from secondary tritons is rather dominant over the low number of primary triton counts. As this background only occurs at low pT,the triton yield is only measured above 2.4 GeV/c(2.0 GeV/cin the most peripheral centrality interval). D. Corrections to the spectra The pT-differential-production spectra of (anti)deuterons, (anti)3He, and (anti)tritons are obtained by correcting the raw spectra for tracking efficiency and acceptance based on MC generated events. The MC samples used to compute the efficiency and the acceptance corrections for the Pb-Pb analysis were generated using the HIJING event generator [74]. Since HIJING does not provide light (anti)nuclei, an ad hoc generator that injects particles on top of the event generator was used. The kinematics of the injected nuclei is chosen randomly by picking their transverse momentum from a flat distribution in the range between 0 and 10 GeV/c, their azimuthal angle from a flat distribution between 0 and 2πradians, and their rapidity from a flat distribution in the range |y|<1. All particles are transported with GEANT4[75] through a full simulation of the ALICE detector. The GEANT4 version used in the ALICE software framework was modified to take into account the latest (anti)nuclei hadronic interaction measurements [24,76]. For the (anti)deuteron, (anti)3He, and (anti)triton analyses, the efficiency×acceptance was determined for each centrality interval separately. The input pTdistributions of (anti)nuclei in the simulation are modified according to a blast-wave (BW) parametrization using pT-dependent weights. The BW parameters are taken from [65]. IV. SYSTEMATIC UNCERTAINTIES The sources of systematic uncertainties affecting these measurements were studied as follows: (1) the amount of material budget employed in the MC simulation of the ALICE apparatus was varied by ± 4.5%, corresponding to the uncertainty on the ALICE material budget determination [67]; (2) track selection criteria were varied as done for previous analyses [21–25]; (3) fit functions used for the signal extraction were varied; (4) for the antitriton analysis different functions were used to weight the input spectra in the simulation. A large contribution of the systematic uncertainty is due to the limited knowledge of the interaction of nuclei with the detector material. The main transport code used in ALICE is GEANT4[75]. This is used to estimate the efficiency×acceptance that is applied as correction to the spectra. In general, the accuracy of the transport codes is limited by the available data for nuclei and especially (anti)nuclei hadronic interaction cross sections, which have only been measured in energy ranges far from the typical momenta of light (anti)nuclei produced in heavy-ion collisions [77–80]. In a detailed study comparing the available data on different targets and their description in GEANT4, the corresponding uncertainty is evaluated as the scaling factor for the cross section value in GEANT4 that is required to match the experimental data. The simulations to estimate the efficiency are 064904-4 LIGHT (ANTI)NUCLEI PRODUCTION IN Pb-Pb … PHYSICAL REVIEW C 107, 064904 (2023) 4− 10 3− 10 2− 10 1− 10 1 10 2 10 /GeV)c) ( T pdyN/(d 2 )d ev N(1/ ALICE | < 0.5y|d 9 2×5%−0 8 2×10%−5 7 2×20%−10 6 2×30%−20 5 2×40%−30 4 2×50%−40 He 3 6− 10 5− 10 4− 10 3− 10 /GeV)c) ( T pdy/(dN 2 )d ev N(1/ t 4 2×5%−0 3 2×10%−5 3 2×10%−0 2 2×30%−10 0123456 )c (GeV/ T p 4− 10 3− 10 2− 10 1− 10 1 10 2 10 /GeV)c) ( T pdy/(dN 2 )d ev N(1/ = 5.02 TeV NN sPb−Pb d 3 2×60%−50 2 2×70%−60 2×80%−70 90%−80 Blast-Wave 01234567 )c (GeV/ T p He 3 01234567 )c (GeV/ T p 6− 10 5− 10 4− 10 3− 10 /GeV)c) ( T pdy/(dN 2 )d ev N(1/ 2×50%−30 90%−50 Blast-Wave t FIG. 4. (Anti)deuteron, (anti)3He, and (anti)tspectra measured in Pb-Pb collisions at √sNN =5.02 TeV for different centrality classes reported with different colours. The boxes represent the systematic uncertainties, while the vertical lines are the statistical ones. The dashed lines represent the individual blast-wave fits to the spectra. The blast-wave fits of (anti)3He are used on (anti)tspectra as well to show the trend. then repeated with the cross section in GEANT4 scaled by this factor. The determined systematic uncertainty is below 1% for the deuterons using TPC and TOF and about 8% for antideuterons at low pT, and decreases down to 4% at the largest pT.For3He it is about 0.5% and for 3He it is about 2% with a small dependence on pT. The values for tand tare similar, with about 0.5% and between 2.5% and 5%, respectively. In addition, weak decays from (anti)hypertritons can affect the (anti)3He spectra and contribute to the systematic uncertainties with about 1.7%. The discrepancy between the data and MC description of the ITS-TPC matching efficiencies is accounted for by adding 5% of systematic uncertainties. All the other systematic uncertainties in the Pb-Pb analyses were estimated separately for each centrality class: particle identification and analysis selection criteria contribute by less than 3%; the signal extraction method by less than 2%; the TPC particle identification systematic uncertainty is estimated to be less than 2%. The huge background and the low number of counts of the (anti)triton analysis result in quite large statistical uncertainties, and the systematic variations were found to be not significant within the statistical uncertainties. Therefore, the uncertainties from the variations were dropped and instead systematic uncertainties based on similar studies for charged pions, kaons, and protons were assigned, namely 5% for the ITS-TPC matching efficiency and 6% for the signal extraction for all centrality and pTintervals. The uncertainty on the pT spectra coming from the uncertainty of the ALICE material budget was determined to be 2% [24]. For the weighting of the efficiency×acceptance, various functional dependencies were applied. This results in a negligible uncertainty in the higher pTintervals, where the weighting does not have any effect, and up to 8% uncertainty in the lower pTintervals. To evaluate the systematic uncertainty due to the background estimation, an alternative data-driven method was used to determine the background. In this method, nontriton candidates were selected in the TPC by requiring that their dE/dx is outside a ±2σwindow around the triton peak. Their squared TOF-mass distribution is used as a template for the background, which is scaled to the squared TOF-mass distribution of triton candidates. It matches very well the background outside the triton peak region and allows an independent estimate of the background under the triton peak. This results in no systematic uncertainty in the low pTregion without any background and up to 20% in the higher pTintervals. All these contributions result in a total systematic uncertainty for the (anti)triton pT spectra between 8% and 22%. V. R E S U LT S The transverse momentum spectra of (anti)deuterons, (anti)3He, and (anti)tritons are extracted in Pb-Pb collisions at √sNN =5.02 TeV for various centrality classes. The transverse momentum spectra are shown in Fig. 4. A clear evolution of the spectral shape with centrality is observed, with the average transverse momentum almost doubling its value going from peripheral to most central Pb-Pb collisions and a shift in the peak position towards higher pTfor increasing multiplicity. 064904-5 S. ACHARYA et al. PHYSICAL REVIEW C 107, 064904 (2023) 0.5 1 1.5 2 2.5 3 )c (GeV/A/ T p 4− 10 3− 10 2− 10 ) 3 c/ 2 (GeV 2 B ALICE | < 0.5y| = 5.02 TeV NN sPb−Pb d 0.5 1 1.5 2 2.5 )c (GeV/A/ T p He 3 0.5 1 1.5 2 2.5 )c (GeV/A/ T p 8− 10 7− 10 6− 10 5− 10 4− 10 ) 6 c/ 4 (GeV 3 B t 0.5 1 1.5 2 2.5 3 )c (GeV/A/ T p 4− 10 3− 10 2− 10 ) 3 c/ 2 (GeV 2 B ALICE 5%−0 10%−5 20%−10 30%−20 40%−30 50%−40 60%−50 70%−60 80%−70 90%−80 | < 0.5y| = 5.02 TeV NN sPb−Pb d 0.5 1 1.5 2 2.5 )c (GeV/A/ T p He 3 0.5 1 1.5 2 2.5 )c (GeV/A/ T p 8− 10 7− 10 6− 10 5− 10 4− 10 ) 6 c/ 4 (GeV 3 B 5%−0 10%−5 10%−0 30%−10 50%−30 90%−50 t FIG. 5. Coalescence parameters B2(left) and B3(right) measured for antinuclei in Pb-Pb collisions at √sNN =5.02 TeV as a function of the transverse momentum scaled by the mass number. Compatible results are obtained for the nuclei. Each color corresponds to a different centrality class. The boxes represent the systematic uncertainties, while the vertical lines are the statistical ones. See the text for details. In order to measure the total yield per rapidity unit in Pb-Pb collisions, the spectra were fitted with the blast-wave function, which assumes a thermal production of particles from an expanding source [81]. The systematic uncertainty of the integrated yield is obtained by shifting the spectrum within its systematic uncertainties and adding an additional uncertainty quadratically to account for the extrapolation to low and high pT. The latter is estimated by using different fit functions such as the mTexponential, Boltzmann, Fermi-Dirac, and Bose- Einstein functions [82]. The fractions of extrapolated yield at low pTfor different centrality classes are about 5% to 40% for (anti)deuterons, 15% (8%) to 50% (35%) for (anti)3He, and 23% (1%) to 50% (11%) for (anti)tritons depending on the centrality class. The extrapolated yields in the high-pT region are negligible for most of the centrality classes except for a 3% contribution for the most peripheral collisions for (anti)deuterons and (anti)3He, and a 55% to 15% contribution depending on the centrality class for (anti)tritons. The statistical uncertainties are calculated by repeating the blast-wave fit by shifting the spectra randomly with a Gaussian distribution within the statistical uncertainties of each pTinterval. The resulting yield distribution is fitted with a Gaussian and the width of this distribution is taken as the statistical uncertainty. The coalescence scenario can be tested by computing the coalescence parameter BA(see for instance Ref. [83] and references therein). Under the assumption of equal production of protons and neutrons, it is defined as BA=EA d3NA dp 3 AEp d3Np dp 3 p−A ,(1) where EAd3NA dp 3 Aand Epd3Np dp 3 pare the invariant production spectra of the nuclei with mass number Aand of protons, respectively. Protons are used here since neutrons are unmeasured and isospin symmetry is expected at LHC energies. Figure 5 shows the measured coalescence parameters B2and B3as a function of the transverse momentum scaled by the mass number Afor Pb-Pb collisions at √sNN =5.02 TeV. An ordering of the coalescence parameters with collision centrality, from higher BAvalues in peripheral collisions to lower BA values in the central ones is clearly visible. This trend with centrality is explained in the coalescence model framework as a consequence of the increasing radius Rof the source from peripheral to central events [44,56,57]. Similarly, the decrease of Rwith increasing momentum as measured with two-proton correlations [84] can also explain the increase of the coalescence parameters with momentum observed in Fig. 5,as already seen in small collision systems [37]. Notably, the space-momentum correlations between nucleons restrict the volume that is effectively used for coalescence and make it smaller than the total volume. This means that particles at higher momentum probe a smaller region in the radially expanding system. The ratio between the production yields of 3He and t provides another powerful test of the coalescence predictions [57]. This model gives two predictions for the formation: one assumes that the A=3 nuclei are formed from three nucleons (called three-body coalescence in the following) and the other assumes the formation of the nucleus from a deuteron and a nucleon (two-body coalescence). Figure 6shows on the left the measured ratios as a function of transverse momentum in different centrality classes. The ratios are flat with pTwithin uncertainties. The average ratio t/3He over the measured transverse momenta is shown in Fig. 6on the right, as a function of the charged-particle multiplicity dNch/dη determined in a pseudorapidity range of |ηlab|<0.5inthe laboratory system. While the SHM expectation for this ratio is very close to 1, the predictions from the coalescence model [57] deviate from unity due to the difference in the wave functions of the two nuclei. However, within the current statistical and systematic uncertainties, it is not possible to conclude which flavor of coalescence model is favoued by the measurement, nor if there is any significant departure from the SHM expectations. Figure 7shows the measured d/p,3He/p, and t/pfor different collision systems at different energies. Both the coalescence models (using the two different approaches, i. e., two-body and three-body coalescence [57], and on top of URQMD [85,86]) and the canonical SHM (CSM) [58] 064904-6 LIGHT (ANTI)NUCLEI PRODUCTION IN Pb-Pb … PHYSICAL REVIEW C 107, 064904 (2023) FIG. 6. Left: ratios of transverse momentum spectra of tand 3He in different centrality intervals. Right: multiplicity dependence of the average t/3He ratio compared with the coalescence model expectations (two-body coalescence in orange and three-body coalescence in blue) [57]. The open boxes represent the total systematic uncertainties, while the vertical lines are the statistical ones. capture qualitatively the observed trend with multiplicity. The UrQMD model uses a hybrid approach where nuclei are ultimately produced by coalescence. However, none of the model curves are able to explain quantitatively all the data points. In all cases, a decrease in the ratios is observed from central Pb-Pb collisions toward peripheral Pb-Pb collisions. In particular, in the case of the d/pratio, this depletion is significant when considering only the uncorrelated uncertainties. Such an effect is expected in transport codes modeling interactions of the nuclei in the rescattering phase following the hadron formation [85]. In the SHM, assuming the grand canonical ensemble, the nucleus-to-proton ratios are fixed by the temperature of the source, thus they are expected to stay constant as a function of charged-particle multiplicity. However, when assuming a canonical ensemble and the exact conservation of baryon number over a defined volume, the nucleus-to-proton ratios increase from low to high multiplicities. The extension of the conservation volume was studied via event-by-event correlation measurement and it was found to be Vc=(1.6± 0.2)dV/dy [25]. The studies presented here thus show that a small conservation volume is needed to describe deuteron-to- 1 10 2 10 3 10 |<0.5 lab η| 〉 lab η/d ch Nd〈 0 2 4 3− 10× )p2 d / (p + = 2.76 TeV NN sPb,−Pb = 5.02 TeV NN sPb,−Pb ALICE | < 0.5yPb: |−pp, Pb < 0yPb: -1 < −p 1 10 2 10 3 10 |<0.5 lab η| 〉 lab η/d ch Nd〈 0 2 4 6 8 10 12 14 16 6− 10× )pHe / (p + 3 2 = 5.02 TeV NN sp-Pb, = 13 TeV, HMspp, = 13 TeVspp, = 7 TeVspp, = 5 TeVspp, 1 10 2 10 3 10 |<0.5 lab η| 〉 lab η/d ch Nd〈 0 2 4 6 8 10 12 14 16 6− 10× )p2 t / (p + = 155 MeV ch TThermal-FIST CSM, y/dV = 1.6 d c V UrQMD Hybrid Coalescence Pb 5.02 TeV−Pb Coalescence Two-body Three-body FIG. 7. Integrated deuteron (left), 3He (middle), and triton yields (right) over proton yields as a function of charged-particle multiplicity dN/dηchfor pp,p-Pb, and Pb-Pb collisions measured by the ALICE Collaboration. The boxes represent the uncorrelated systematic uncertainties, while the vertical lines are the statistical ones. The shaded boxes represent the centrality-correlated uncertainties. In addition, the data are compared to the THERMAL-FIST CSM (canonical statistical model) at 155 MeV with a correlation volume of Vc=1.6dV/dy shown as ablackline[58], the two coalescence approaches displayed in green (two-body coalescence) and in blue (three-body coalescence) [57], and URQMD hybrid coalescence shown as a purple line [86]. 064904-7 S. ACHARYA et al. PHYSICAL REVIEW C 107, 064904 (2023) proton ratio in peripheral Pb-Pb collisions within the SHM, while the production of protons requires significantly larger values of around Vc=(3–5)dV/dy [61]. At the moment, there is no configuration of the SHM that is able to describe simultaneously protons and nuclei with a single set of parameters in peripheral Pb-Pb and smaller collision systems. The decrease of the nucleus over proton ratios going towards smaller multiplicities is also expected in coalescence models, where it is caused by the evolution of the system size with multiplicity. VI. SUMMARY AND CONCLUSION In this article, we have presented comprehensive measurements of the production of (anti)nuclei in Pb-Pb collisions at √sNN =5.02 TeV including the first antitriton measurement in Pb-Pb collisions at LHC energies. The obtained results follow the trends established at lower collision energy, but show a much larger constraining power on models thanks to significantly smaller systematic and statistical uncertainties. For deuterons, the number of studied centrality intervals was largely increased compared to previous ALICE studies and demonstrate the strong increase of the radial flow when going from peripheral to central events. This is similarly visible for 3He and t, but with a lower number of centrality intervals. The extracted spectra for tand 3He agree well in the overlap region of both spectra. Only for the most peripheral interval a slight deviation from unity is visible, which is also expected by coalescence models, where the deviation at low multiplicities is expected due to the different spatial wave functions of tand 3He [44,57]. This will be constrained better with high-statistics data from Run 3, using all available collision systems, i. e., pp,p-Pb, and Pb-Pb. The yield ratios of d/pas a function of charged-particle multiplicity agree well with both expectations, i. e., coalescence and thermal models. Notably, the deuteron-over-proton ratio requires a small correlation volume within the SHM with respect to net-proton fluctuation measurements. For 3He the data lie at low multiplicity slightly closer to the coalescence expectations, and for high multiplicities corresponding to Pb- Pb the data lie between thermal and coalescence models. In contrast, for the triton the data points are much closer to the coalescence model with multiplicities in Pb-Pb collisions. Recently, several works appeared [87–89] that each try to improve the SHM in particular multiplicity regions. They give a good description in the region they are applied to, but they are not applicable in the full multiplicity range investigated here. The presented data, even though they are much more precise than previous results, still do not allow for a strong conclusion about the dominant production mechanism. More differential studies, in particular also those involving additional (hyper)nuclei, such as 4He and 3 H, will help us to understand better the processes underlying the formation of composite objects. The ongoing Run 3 of the LHC with the upgraded ALICE apparatus will allow for such more precise studies of (anti)(hyper)nuclei production and for the extension to mass A=4 hypernuclei in Pb-Pb collisions [90]. ACKNOWLEDGMENTS The ALICE Collaboration would like to thank all its engineers and technicians for their invaluable contributions to the construction of the experiment and the CERN accelerator teams for the outstanding performance of the LHC complex. The ALICE Collaboration gratefully acknowledges the resources and support provided by all Grid centres and the Worldwide LHC Computing Grid (WLCG) Collaboration. The ALICE Collaboration acknowledges the following funding agencies for their support in building and running the ALICE detector: A. I. Alikhanyan National Science Laboratory (Yerevan Physics Institute) Foundation (ANSL), State Committee of Science, and World Federation of Scientists (WFS), Armenia; Austrian Academy of Sciences, Austrian Science Fund (FWF) [M 2467-N36] and Nationalstiftung für Forschung, Technologie und Entwicklung, Austria; Ministry of Communications and High Technologies, National Nuclear Research Center, Azerbaijan; Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq), Financiadora de Estudos e Projetos (Finep), Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP), and Universidade Federal do Rio Grande do Sul (UFRGS), Brazil; Bulgarian Ministry of Education and Science, within the National Roadmap for Research Infrastructures 2020–2027 (object CERN), Bulgaria; Ministry of Education of China (MOEC), Ministry of Science & Technology of China (MSTC), and National Natural Science Foundation of China (NSFC), China; Ministry of Science and Education and Croatian Science Foundation, Croatia; Centro de Aplicaciones Tecnológicas y Desarrollo Nuclear (CEADEN), Cubaenergía, Cuba; Ministry of Education, Youth and Sports of the Czech Republic, Czech Republic; The Danish Council for Independent Research–Natural Sciences, the VILLUM FONDEN, and Danish National Research Foundation (DNRF), Denmark; Helsinki Institute of Physics (HIP), Finland; Commissariat à l’Energie Atomique (CEA) and Institut National de Physique Nucléaire et de Physique des Particules (IN2P3) and Centre National de la Recherche Scientifique (CNRS), France; Bundesministerium für Bildung und Forschung (BMBF) and GSI Helmholtzzentrum für Schwerionenforschung GmbH, Germany; General Secretariat for Research and Technology, Ministry of Education, Research and Religions, Greece; National Research, Development and Innovation Office, Hungary; Department of Atomic Energy Government of India (DAE), Department of Science and Technology, Government of India (DST), University Grants Commission, Government of India (UGC), and Council of Scientific and Industrial Research (CSIR), India; National Research and Innovation Agency–BRIN, Indonesia; Istituto Nazionale di Fisica Nucleare (INFN), Italy; Japanese Ministry of Education, Culture, Sports, Science and Technology (MEXT) and Japan Society for the Promotion of Science (JSPS) KAKENHI, Japan; Consejo Nacional de Ciencia (CONACYT) y Tecnología, through Fondo de Cooperación Internacional en Ciencia y Tecnología (FONCICYT) and Dirección General de Asuntos del Personal Academico (DGAPA), Mexico; Nederlandse Organisatie voor Wetenschappelijk Onderzoek (NWO), Netherlands; The Research Council of Norway, Norway; Commission on Science 064904-8 LIGHT (ANTI)NUCLEI PRODUCTION IN Pb-Pb … PHYSICAL REVIEW C 107, 064904 (2023) 41Department of Physics, Gauhati University, Guwahati, India 42Helmholtz-Institut für Strahlen- und Kernphysik, Rheinische Friedrich-Wilhelms-Universität Bonn, Bonn, Germany 43Helsinki Institute of Physics (HIP), Helsinki, Finland 44High Energy Physics Group, Universidad Autónoma de Puebla, Puebla, Mexico 45Horia Hulubei National Institute of Physics and Nuclear Engineering, Bucharest, Romania 46Indian Institute of Technology Bombay (IIT), Mumbai, India 47Indian Institute of Technology Indore, Indore, India 48INFN, Laboratori Nazionali di Frascati, Frascati, Italy 49INFN, Sezione di Bari, Bari, Italy 50INFN, Sezione di Bologna, Bologna, Italy 51INFN, Sezione di Cagliari, Cagliari, Italy 52INFN, Sezione di Catania, Catania, Italy 53INFN, Sezione di Padova, Padova, Italy 54INFN, Sezione di Pavia, Pavia, Italy 55INFN, Sezione di Torino, Turin, Italy 56INFN, Sezione di Trieste, Trieste, Italy 57Inha University, Incheon, Republic of Korea 58Institute for Gravitational and Subatomic Physics (GRASP), Utrecht University/Nikhef, Utrecht, Netherlands 59Institute of Experimental Physics, Slovak Academy of Sciences, Košice, Slovak Republic 60Institute of Physics, Homi Bhabha National Institute, Bhubaneswar, India 61Institute of Physics of the Czech Academy of Sciences, Prague, Czech Republic 62Institute of Space Science (ISS), Bucharest, Romania 63Institut für Kernphysik, Johann Wolfgang Goethe-Universität Frankfurt, Frankfurt, Germany 64Instituto de Ciencias Nucleares, Universidad Nacional Autónoma de México, Mexico City, Mexico 65Instituto de Física, Universidade Federal do Rio Grande do Sul (UFRGS), Porto Alegre, Brazil 66Instituto de Física, Universidad Nacional Autónoma de México, Mexico City, Mexico 67iThemba LABS, National Research Foundation, Somerset West, South Africa 68Jeonbuk National University, Jeonju, Republic of Korea 69Fachbereich Informatik und Mathematik, Johann-Wolfgang-Goethe Universität Frankfurt Institut für Informatik, Frankfurt, Germany 70Korea Institute of Science and Technology Information, Daejeon, Republic of Korea 71KTO Karatay University, Konya, Turkey 72Laboratoire de Physique des 2 Infinis, Irène Joliot-Curie, Orsay, France 73Laboratoire de Physique Subatomique et de Cosmologie, Université Grenoble-Alpes, CNRS-IN2P3, Grenoble, France 74Lawrence Berkeley National Laboratory, Berkeley, California, USA 75Division of Particle Physics, Department of Physics, Lund University, Lund, Sweden 76Nagasaki Institute of Applied Science, Nagasaki, Japan 77Nara Women’s University (NWU), Nara, Japan 78Department of Physics, School of Science, National and Kapodistrian University of Athens, Athens, Greece 79National Centre for Nuclear Research, Warsaw, Poland 80National Institute of Science Education and Research, Homi Bhabha National Institute, Jatni, India 81National Nuclear Research Center, Baku, Azerbaijan 82National Research and Innovation Agency - BRIN, Jakarta, Indonesia 83Niels Bohr Institute, University of Copenhagen, Copenhagen, Denmark 84Nikhef, National Institute for Subatomic Physics, Amsterdam, Netherlands 85Nuclear Physics Group, STFC Daresbury Laboratory, Daresbury, United Kingdom 86Nuclear Physics Institute of the Czech Academy of Sciences, Husinec- ˇ Rež, Czech Republic 87Oak Ridge National Laboratory, Oak Ridge, Tennessee, USA 88Ohio State University, Columbus, Ohio, USA 89Physics Department, Faculty of science, University of Zagreb, Zagreb, Croatia 90Physics Department, Panjab University, Chandigarh, India 91Physics Department, University of Jammu, Jammu, India 92Physics Program and International Institute for Sustainability with Knotted Chiral Meta Matter (SKCM2), Hiroshima University, Hiroshima, Japan 93Physikalisches Institut, Eberhard-Karls-Universität Tübingen, Tübingen, Germany 94Physikalisches Institut, Ruprecht-Karls-Universität Heidelberg, Heidelberg, Germany 95Physik Department, Technische Universität München, Munich, Germany 96Politecnico di Bari and Sezione INFN, Bari, Italy 97Research Division and ExtreMe Matter Institute EMMI, GSI Helmholtzzentrum für Schwerionenforschung GmbH, Darmstadt, Germany 98Saga University, Saga, Japan 064904-15 S. ACHARYA et al. PHYSICAL REVIEW C 107, 064904 (2023) 99Saha Institute of Nuclear Physics, Homi Bhabha National Institute, Kolkata, India 100School of Physics and Astronomy, University of Birmingham, Birmingham, United Kingdom 101Sección Física, Departamento de Ciencias, Pontificia Universidad Católica del Perú, Lima, Peru 102Stefan Meyer Institut für Subatomare Physik (SMI), Vienna, Austria 103SUBATECH, IMT Atlantique, Nantes Université, CNRS-IN2P3, Nantes, France 104Sungkyunkwan University, Suwon City, Republic of Korea 105Suranaree University of Technology, Nakhon Ratchasima, Thailand 106Technical University of Košice, Košice, Slovak Republic 107The Henryk Niewodniczanski Institute of Nuclear Physics, Polish Academy of Sciences, Cracow, Poland 108The University of Texas at Austin, Austin, Texas, USA 109Universidad Autónoma de Sinaloa, Culiacán, Mexico 110Universidade de São Paulo (USP), São Paulo, Brazil 111Universidade Estadual de Campinas (UNICAMP), Campinas, Brazil 112Universidade Federal do ABC, Santo Andre, Brazil 113University of Cape Town, Cape Town, South Africa 114University of Houston, Houston, Texas, USA 115University of Jyväskylä, Jyväskylä, Finland 116University of Kansas, Lawrence, Kansas, USA 117University of Liverpool, Liverpool, United Kingdom 118University of Science and Technology of China, Hefei, China 119University of South-Eastern Norway, Kongsberg, Norway 120University of Tennessee, Knoxville, Tennessee, USA 121University of the Witwatersrand, Johannesburg, South Africa 122University of Tokyo, Tokyo, Japan 123University of Tsukuba, Tsukuba, Japan 124University Politehnica of Bucharest, Bucharest, Romania 125Université Clermont Auvergne, CNRS/IN2P3, LPC, Clermont-Ferrand, France 126Université de Lyon, CNRS/IN2P3, Institut de Physique des 2 Infinis de Lyon, Lyon, France 127Université de Strasbourg, CNRS, IPHC UMR 7178, F-67000 Strasbourg, France, Strasbourg, France 128Départment de Physique Nucléaire (DPhN), IRFU, Université Paris-Saclay Centre d’Etudes de Saclay (CEA), Saclay, France 129Università degli Studi di Foggia, Foggia, Italy 130Università del Piemonte Orientale, Vercelli, Italy 131Università di Brescia, Brescia, Italy 132Variable Energy Cyclotron Centre, Homi Bhabha National Institute, Kolkata, India 133Warsaw University of Technology, Warsaw, Poland 134Wayne State University, Detroit, Michigan, USA 135Westfälische Wilhelms-Universität Münster, Institut für Kernphysik, Münster, Germany 136Wigner Research Centre for Physics, Budapest, Hungary 137Yale University, New Haven, Connecticut, USA 138Yonsei University, Seoul, Republic of Korea 139Zentrum für Technologie und Transfer (ZTT), Worms, Germany 140Affiliated with an institute covered by a cooperation agreement with CERN 141Affiliated with an international laboratory covered by a cooperation agreement with CERN *Also at Max-Planck-Institut für Physik, Munich, Germany. †Also at Italian National Agency for New Technologies, Energy and Sustainable Economic Development (ENEA), Bologna, Italy. ‡Also at Dipartimento DET del Politecnico di Torino, Turin, Italy. §Deceased Also at An institution covered by a cooperation agreement with CERN. ¶Also at Department of Applied Physics, Aligarh Muslim University, Aligarh, India. **Also at Institute of Theoretical Physics, University of Wroclaw, Poland. ††Also at Indian Institute of Science Education and Research (IISER) Berhampur, Odisha, India. 064904-16