Energy dependence of light hypernuclei production in heavy-ion collisions from a coalescence and statistical-thermal model perspective Tom Reichert1 2Jan Steinheimer3Volodymyr Vovchenko4 3Benjamin D onigus5and Marcus Bleicher1 2

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Energy dependence of light hypernuclei production in heavy-ion collisions

from a coalescence and statistical-thermal model perspective

Tom Reichert,1, 2 Jan Steinheimer,3Volodymyr Vovchenko,4, 3 Benjamin D¨onigus,5and Marcus Bleicher1, 2

1Institut f¨ur Theoretische Physik, Goethe Universit¨at Frankfurt,

Max-von-Laue-Str. 1, D-60438 Frankfurt am Main, Germany

2Helmholtz Research Academy Hesse for FAIR (HFHF),

GSI Helmholtzzentrum f¨ur Schwerionenforschung GmbH, Campus Frankfurt,

Max-von-Laue-Str. 12, 60438 Frankfurt am Main, Germany

3Frankfurt Institute for Advanced Studies, Ruth-Moufang-Str. 1, D-60438 Frankfurt am Main, Germany

4Institute for Nuclear Theory, University of Washington, Seattle, WA 98195-1550, USA

5Institut f¨ur Kernphysik, Goethe Universit¨at Frankfurt,

Max-von-Laue-Str. 1, D-60438 Frankfurt am Main, Germany

(Dated: February 28, 2023)

A comparison of light hypernuclei production, from UrQMD+coalescence and the thermal model,

in heavy ion collisions over a wide range of beam energies and system sizes is presented. We ﬁnd that

both approaches provide generally similar results, with diﬀerences in speciﬁc details. Especially the

ratios of hypertriton to Λ are aﬀected by both the source radius ∆rof the coalescence procedure as

well as canonical eﬀects. On the other hand, the double ratio S3is almost independent of canonical

eﬀects, which is in contrast to coalescence. Thus, both the beam energy dependence and centrality

dependence of S3can be used to constrain the hypertriton source radius. To do so the currently

available data is not yet suﬃcient. Elliptic ﬂow is shown to be unaﬀected by the source size of the

nuclei and an almost perfect mass scaling of the elliptic ﬂow is observed. Our predictions further

suggest that the existence of the H-dibaryon (ΛΛ) seems ruled out by ALICE data.

I. INTRODUCTION

Hypernuclei, ordinary nuclei with at least one bound

hyperon, are an important topic of nuclear physics [1].

Understanding the creation and properties of hypernu-

clei can help in the understanding of the strong inter-

action and the role of ﬂavor symmetry, relevant for nu-

clear structure but also the nuclear equation of state at

high density. Heavy-ion reactions at relativistic energies

are an abundant source of strangeness and therefore well

suited for the production of light hypernuclei.

Recently, several heavy-ion experiments have pub-

lished data on the production of (anti-)hypernuclei and

on their properties, e.g. the lifetime [2–9].

The lifetime measured in these experiments was found

to be signiﬁcantly below the free Λ lifetime which was not

expected from Faddeev-type calculations [10,11]. This

lead to the so-called hypertriton puzzle, i.e. a signiﬁcant

deviation of the hypertriton (3

ΛH) lifetime from the life-

time of the free Λ. Currently, the tension between this

expectation and the data is about 4.2σ[12,13]. Never-

theless, the measured properties of the hypertriton lead

to consequences also for its production.

In particular, it was suggested that the speciﬁc struc-

ture of the hypertriton, i.e. a small deuteron core with

a weakly bound Λ (BΛ= 0.162 ±0.044 MeV [14], BΛ

being the so-called Λ separation energy), would lead to

observable consequences in the system size dependence

of hypertriton production [15].

Since measurements of hypernuclei are yet scarce and

done at widely varying beam energies, it can be useful

to investigate their production properties in models that

can span such a big range of energies and system sizes

in a consistent manner. Then systematic trends in the

dependence of the hypernuclei production on its proper-

ties can be extracted. In this work, we will attempt just

that and present calculations of light single and doubly-

strange hypernuclei in heavy-ion collisions over a broad

range of beam energies and system sizes. For a complete

picture we will compare production rates from a (canoni-

cal) thermal model (Thermal-FIST) with those obtained

from a coalescence model based on freeze-out distribu-

tions modeled with the UrQMD (hybrid-)model. Finally,

we identify an observable which shows the most promis-

ing dependence on the hypernuclei production properties.

II. METHODS

To make realistic predictions for the production rates

and properties of hypernuclei, dynamic simulations are

necessary. Since we want to study a broad range of beam

energies and system sizes we will employ the UrQMD

transport model to simulate the underlying hadron phase

space distributions. The UrQMD model is a microscopic

transport model based on the propagation and 2-body

scattering of hadrons according to a geometrical inter-

pretation of the scattering cross sections [16,17]. For

beam energies of √sNN <10 GeV, this model provides

a good description of experimental observables and mea-

sured hadron spectra in heavy ion collisions. For higher

beam energies the model signiﬁcantly underestimates the

ﬂow created [18] as well as the strangeness produced [19]

which is why a so-called hybrid-model was established

in which the dense phase is described by an ideal ﬂuid

dynamical simulation [20].

arXiv:2210.11876v2 [nucl-th] 27 Feb 2023

In the hybrid description, the transition from the ﬂuid

description back to the transport description occurs on

an iso-energy-density hypersurface = 30, where 0≈

145 MeV/fm3. The hypersurface is then used to sample

hadrons according to the Cooper-Frye equation [21,22]

which then continue to interact within the cascade part

of the UrQMD model, until reactions cease and kinetic

freeze-out is reached. For the hydro part we use an equa-

tion of state that contains a smooth crossover between

a hadron resonance gas and a deconﬁned quark-gluon-

plasma [23].

A. Thermal model

The thermal model of particle production in heavy-

ion collisions assumes that their primordial abundances

are ﬁxed at the stage of chemical freeze-out and corre-

spond to the hadron resonance gas model in chemical

equilibrium [24,25]. The only changes to the ﬁnal abun-

dances come from decay feed-down. The model param-

eters – the temperature T, baryochemical potential µB,

and the freeze-out volume V– are extracted at each col-

lision energy by ﬁtting the experimental data. The ther-

mal model is used to describe light (anti-)(hyper-)nuclei

production by incorporating these objects as explicit de-

grees of freedom in the partition function [26,27]. Under

the assumption that chemical freeze-out of light nuclei

happens simultaneously with other hadrons1, the model

provides predictions for light nuclei abundances in cen-

tral collisions of heavy ions without introducing further

parameters. In many cases, the model shows good agree-

ment with the experiment [30,31]. Augmented with the

canonical treatment of baryon number conservation, the

model can also describe features of light nuclei produc-

tion in small systems at the LHC [32].

In the present work, we confront the predictions of

the UrQMD coalescence approach both with the ther-

mal model and experimental data. For making predic-

tions of the midrapidity yields dN/dy at various colli-

sion energies, one has to specify the thermal model pa-

rameters T,µB, and Vas a function of √sNN. To this

end, we utilize the chemical freeze-out curve of Ref. [33]

which parameterizes the collision energy dependence of

the temperature and baryochemical potential, T(√sNN)

and µB(√sNN). In principle, this parametrization is

suﬃcient to study the collision energy dependence of

any yield ratio since the remaining volume parameter

V(√sNN) cancels out in any such ratio. Nevertheless, it

can also be helpful to study thermal model predictions for

absolute yields, for which one has to additionally specify

the V(√sNN) dependence. We ﬁx V(√sNN) for 0-5% cen-

tral Au-Au/Pb-Pb collisions in the following way. First,

we use the world data [34–39] on the collision energy de-

pendence of charged pion multiplicity to parameterize its

collision energy dependence from 2.4 GeV to 5.02 TeV.

We take a ﬁt function from [40] where it was used to pa-

rameterize the energy dependence of charged multiplicity.

The ﬁt to the pion data yields

dNπ+

dy +dNπ−

dy =a sb

NN ln(sNN)−c. (1)

Here sNN is in the units of GeV2, and the parameter val-

ues are a= 49.84903, b= 0.04110131, and c= 61.48846.

Then, at each √sNN we ﬁx V(√sNN) to a value such

that the thermal model reproduces dNπ+

dy +dNπ

−

dy from

Eq. (1). We also check that total baryon number dNB/dy

calculated at a given energy does not exceed the number

of participants, Npart = 360. If it does, the volume is

rescaled down such that dNB/dy =Npart. This rescaling

is only necessary at very low energies, √sNN .2.8 GeV.

The eﬀect of exact local conservation of strangeness

becomes important for strange particles, such as hyper-

nuclei, at low collision energies where the amount of

the produced strangeness is small. Here we incorporate

this eﬀect through the strangeness-canonical ensemble,

which enforces the exact conservation of net strangeness

in a correlation volume Vc. We take a correlation radius

Rc= 2.4 fm (Vc=4π

3R3

c), as inferred from the recent

measurements of the φ/K−ratio at √sNN = 3 GeV [41].

We also use the thermal model to study the system-

size dependence of light (anti-)(hyper-)nuclei ratios at

LHC energies. Canonical suppression eﬀects drive this

dependence. Here we use the canonical statistical model

of Ref. [32], with a constant temperature T= 155 MeV

across all multiplicities, and the canonical correlation vol-

ume of Vc= 1.6dV/dy suggested by recent measurements

of antiproton-antideuteron correlations [42].

All our thermal model calculations are performed using

the open-source Thermal-FIST package [43]. These cal-

culations optionally include feed-down from the decays

of excited nuclei, as described in [44].

B. Coalescence approach

The coalescence approach to (hyper-)nuclei production

assumes that these nuclei are produced after the kinetic

freeze-out (last scattering or decay) of their constituents

[45–61]. If the full phase space information on the nucle-

ons and hyperons at this time is known, the probability

of a pair or triplet of baryons forming a bound nucleus

can be estimated from the coalescence formula [62]

1This assumption can be relaxed to allow light nuclei production

at later stages, if one takes partial chemical equilibrium into account. In such a scenario one obtains similar results as in the

standard thermal model [28,29].

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Energydependenceoflighthypernucleiproductioninheavy-ioncollisionsfromacoalescenceandstatistical-thermalmodelperspectiveTomReichert,1,2JanSteinheimer,3VolodymyrVovchenko,4,3BenjaminDonigus,5andMarcusBleicher1,21InstitutfurTheoretischePhysik,GoetheUniversitatFrankfurt,Max-von-Laue-Str.1,D-60438Fran...

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Energy dependence of light hypernuclei production in heavy-ion collisions from a coalescence and statistical-thermal model perspective Tom Reichert1 2Jan Steinheimer3Volodymyr Vovchenko4 3Benjamin D onigus5and Marcus Bleicher1 2

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