Momentum and multiplicity dependence of strangeness and nuclei production

Prominent phenomena observed in high-energy hadronic collisions, 6 such as the strangeness enhancement in small collision systems with increas7 ing multiplicity and the production of loosely bound states in collisions where 8 extreme temperatures are reached, are still mysterious and at the center of the 9 experimental programs of several scientific Collaborations. In this contribution, 10 recent experimental results from the ALICE and STAR Collaborations on these 11 two fronts are presented and discussed. 12 1 Strangeness enhancement 13 One of the most intriguing observations in the research field dedicated to the study of 14 strangeness production in high-energy hadronic collisions is the continuous evolution of the 15 ratio between (multi)strange hadron yields and pion yields with increasing charged-particle 16 multiplicity at mid-rapidity 〈dNch/dη〉|η|<0.5 [1, 2]. The measured ratios show an increase for 17 〈dNch/dη〉|η|<0.5 50 which is followed by a saturation for higher multiplicities, up to the 18 most central nucleus–nucleus collisions at the LHC. This behavior seems to be independent 19 of the collision system and the center-of-mass energy of the collision. A larger increase is 20 observed for hadrons with larger strangeness content. The origin of strangeness enhancement 21 is still not fully understood from the theoretical point of view and different approaches are 22 used to describe the experimental observations. Three of the most used models are presented 23 in the following. 24 In the Canonical Statistical Model (CSM) [3], the multiplicity dependence of strange 25 hadron to pion ratios emerges from the exact conservation of electric charge, baryon number, 26 and strangeness in the so-called correlation volume Vc. In the perspective of this model, the 27 strangeness enhancement with increasing multiplicity is rather seen as a strangeness suppres28 sion with respect to the grand-canonical limit, reached in central nucleus–nucleus collisions, 29 going to lower multiplicities. Recent developments of this model include a multiplicity30 dependent chemical freeze-out temperature Tchem and the assumption of an incomplete chem31 ical equilibration described by a multiplicity-dependent strangeness saturation parameter γS 32 [3]. This model provides a good description of the available data except for the p/π ratio, 33 which is overestimated by approximately 2σ at all multiplicities [3]. In the two-component 34 “core-corona” model [4], the smooth evolution from the string fragmentation regime in pp 35 collisions to statistical hadronization in nucleus–nucleus collisions is interpreted as an in36 crease of the relative contribution from the high-density “core” with increasing multiplicity. 37 ∗e-mail: alberto.caliva@cern.ch © The Authors, published by EDP Sciences. This is an open access article distributed under the terms of the Creative Commons Attribution License 4.0 (http://creativecommons.org/licenses/by/4.0/). EPJ Web of Conferences 259, 03004 (2022) https://doi.org/10.1051/epjconf/202225903004 SQM 2021

used to describe the experimental observations. Three of the most used models are presented 23 in the following. 24 In the Canonical Statistical Model (CSM) [3], the multiplicity dependence of strange 25 hadron to pion ratios emerges from the exact conservation of electric charge, baryon number, 26 and strangeness in the so-called correlation volume V c . In the perspective of this model, the 27 strangeness enhancement with increasing multiplicity is rather seen as a strangeness suppres-28 sion with respect to the grand-canonical limit, reached in central nucleus-nucleus collisions, 29 going to lower multiplicities. Recent developments of this model include a multiplicity-30 dependent chemical freeze-out temperature T chem and the assumption of an incomplete chem-31 ical equilibration described by a multiplicity-dependent strangeness saturation parameter γ S 32 Strangeness enhancement can also be described in the context of the Lund string fragmen-38 tation model using high-density color strings (ropes) and the color reconnection mechanism 39 [5]. The role of canonical suppression becomes relevant also at low center-of-mass energy col-42 lisions. This is nicely highlighted by the measurements of φ/K − and φ/Ξ − as a function of 43 centrality and center-of-mass energy by the STAR Collaboration (Fig. 1) Figure 1. φ/K − and φ/Ξ − measured as a function of the center-of-mass energy in different collision systems by the STAR Collaboration.

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Strangeness enhancement is further studied by the ALICE Collaboration as a function of ef-53 fective energy. This is the energy effectively available for particle production at mid-rapidity 54 considering that a fraction of the initial center-of-mass energy is carried away by baryons 55 emitted at forward rapidity. Their energy is measured using the Zero-Degree Calorimeters  = 13 TeV. The two-particle correlation method is used in this measurement to distinguish 65 the different contributions: a charged particle with the highest p T and p T > 3 GeV/c, called 66 "trigger particle", is used as a proxy for the jet. The "in-jet" and "out-of-jet" regions are    [12]. Multi-baryon states are assumed to be produced as compact multi-quark systems, which 83 evolve towards the final configuration with typical timescales of 5 fm/c or longer [12]. This 84 model provides an excellent description of the measured hadron yields in central nucleus-85 nucleus collisions [12]. In the coalescence model [14][15][16][17][18][19], multi-baryon states are assumed 86 to be formed by coalescence of baryons that are close in phase space at kinetic freeze-out.

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In the state-of-the-art implementations of the coalescence approach, the quantum-mechanical From systematic studies of light (anti-)nuclei production in hadronic collisions at different 92 multiplicities, it seems that the dominant production mechanism evolves smoothly from small 93 to large collision systems with the charged-particle multiplicity. A smooth transition from 94 the low-multiplicity regime towards the grand-canonical limit is observed in the yield ratios 95 d/p and 3 He/p. While the multiplicity evolution of the d/p ratio is fairly well reproduced 96 by the coalescence model [19], some tensions are observed in the intermediate multiplicity all multiplicities [11], provides only a qualitative description of these data. A continuous 99 evolution with multiplicity is also observed for the coalescence parameter, defined as the 100 ratio between the invariant yield of a nucleus with a mass number A and that of protons 101 to the power of A. In particular, the coalescence parameters for a fixed p T /A continuously 102 decrease going from pp to central nucleus-nucleus collisions. In the coalescence approach, 103 this behavior is connected to the multiplicity evolution of the particle-emitting source size 104 [16]: nucleons with fixed p T /A are, on average, closer in space in small systems as compared 105 to large systems, hence the coalescence probability in small systems is larger.

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The deuteron production is studied by the ALICE Collaboration in jets and in the UE in pp 108 collisions at √ s = 13 TeV [20]. The p T -differential jet-associated deuteron production is 109 measured using the two-particle correlation method as described in Sect. 1.3. The p T spec-110 trum of deuterons inside the jets is found to be consistent with predictions based on PYTHIA 111 coupled to a simple coalescence afterburner. In the latter, deuteron formation is assumed to 112 happen if a proton and neutron have a momentum difference ∆p < p 0 , with p 0 =110 MeV, 113 thus ignoring the space coordinates in the calculation of the coalescence probability.

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The deuteron p T spectra are also studied in the jet region and in the UE as a function of the 115 EU activity. The latter is quantified by the ratio R T = N T ch / N T ch , where N T ch is the charged-116 particle multiplicity measured in the transverse region with respect to the trigger particle.  The radial extension of the hypertriton wave function, constrained by the lifetime and 139 Λ separation energy measurements, is a relevant parameter in the coalescence model which 140 enters explicitly into the coalescence probability [19]. On the contrary, the predictions from 141 the statistical hadronization model are independent of the system size and depend only on the 142 mass and spin of the bound state [8][9][10][11][12][13]. The hypertriton yield measured in central nucleus-143 nucleus collisions, both at low and high center-of-mass energy, are consistent with the thermal 144 model (Fig. 6 left). On the other hand, recent measurements of the hypertriton production in small collision systems by the ALICE Collaboration favor the two-body coalescence model. 146 The preliminary measurement of the 4 Λ H -a bound state with two protons, a neutron and a Λ 147 -in central Au-Au collisions at 3 GeV challenges both models (Fig. 6 right).
148 Figure 6. Hypertriton (left) and 4 Λ H yield (right) as a function of the center-of-mass energy.