Predictions for production of 3 Λ H and 3 Λ ¯ ¯ ¯ ¯ H ¯ ¯ ¯ ¯ in isobaric 96 44 Ru+ 96 44 Ru and 96 40 Zr+ 96 40 Zr collisions at s NN − − − √ = 200 GeV
Zhi-Lei She, Gang Chen, Dai-Mei Zhou, Liang Zheng, Yi-Long Xie, Hong-Ge Xu
aa r X i v : . [ nu c l - t h ] S e p Predictions for production of H and H in isobaric Ru+
Ru and
Zr+
Zrcollisions at √ s NN = 200 GeV Zhi-Lei She , , Gang Chen , ∗ , Dai-Mei Zhou , Liang Zheng , Yi-Long Xie , Hong-Ge Xu Institute of Geophysics and Geomatics, China University of Geosciences, Wuhan,430074, China. School of Mathematics and Physics, China University of Geosciences, Wuhan,430074, China. Institute of Particle Physics, Central China Normal University, Wuhan 430079, China.
The production of H and H, as well as H, H, He, and He are studied in central collisionsof isobars
Ru+
Ru and
Zr+
Zr at √ s NN = 200 GeV, using the dynamically constrainedphase-space coalescence model along with the PACIAE model simulations. It is found that the yieldratios of H to H and H, He to H, He, coalescence parameter √ B , strangeness populationfactor s of (anti-)hypertriton and light (anti-)nuclei are all the same within uncertainty althoughthe yield of (anti-)hypertriton ( H , H) is less than that of light (anti-)nuclei ( H, He, H, He),respectively. However there is no difference in the yield, yield ratio, coalescence parameters, andstrangeness population factor of (anti-)hypertriton and (anti-)nuclei produced in isobaric
Ru+
Ruand
Zr+
Zr collisions. Experimental data of Cu+Cu, Au+Au and Pb+Pb collisions from RHIC,ALICE are presented in the results for comparison.
I. INTRODUCTION
The high-energy heavy ion collisions can create aunique opportunity to study the behaviour of light (anti-)nuclei and (anti-)hypernuclei produced under condi-tions of extreme high temperatures and energy densi-ties. In these collisions, plenty of (anti-)nuclei and (anti-)hypernuclei consisted of (anti-)nucleons and/or (anti-)hyperons are are created, which attracts a constant in-terest in studying antimatter and exploring fundamentalproblems in physics [1, 2]. For example, the fundamen-tal CPT theorem can be tested by the precision mea-surement of the mass difference between nuclei and anti-nuclei [3] or the difference of the mass, lifetime and bind-ing energy of the hypertriton ( H) and its correspondinganti-hypertriton ( H) [4, 5] in Au+Au and Pb+Pb col-lision systems.The anti-hypertriton ( H), the lightest bound antihy-pernucleus, consists of a anti-hyperon Λ , a antiproton p , and a antineutron n , which had been discovered inAu+Au collisions at √ s NN = 200 GeV by STAR Col-laboration at the BNL Relativistic Heavy Ion Collider(RHIC) [6] and then in Pb+Pb collisions at √ s NN = 2 . H ( H) has distinct features in heavy-ion collisionscompared with corresponding normal three-body (anti-)nuclei He ( He) and H ( H), due to the different inter-action strength between hyperon-nucleon and nucleon-nucleon [8]. Hence some theoretical approaches on theproduction of H ( H) in heavy-ion reactions have beenproposed, where the production mechanism has usuallybeen described either by statistical thermal methods [9–14] or a coalescence model [15–20].The existence of H ( H) in heavy-ion reactions are ∗ Corresponding Author: [email protected] observed, ranging from AGS [21] up to RHIC [6, 20]and LHC [7] collision energies, involving various colli-sion systems, such as Cu+ Cu,
Au+
Au, and
Pb+
Pb collisions [1, 2]. One can see that there ex-ists an empty space of the system size for nucleus-nucleusinteractions between Cu+ Cu and
Au+
Au col-lisions, i.e., no data for the medium-heavy nucleus.However, the recent isobaric collision experiment of
Ru+
Ru and
Zr+
Zr at √ s NN = 200 GeV can beused to fill the gap of system size in the above, althoughthis isobar program was originally proposed to search forthe presence of Chiral Magnetic Effect (CME) [22–25].In this paper, the production of the final state hadrons,including p , p , Λ, and Λ, are simulated by the parton andhadron cascade model ( PACIAE ) [26] in
Ru+
Ru and
Zr+
Zr at the top RHIC energy of √ s NN = 200 GeVwith midrapidity ( | η | < DCPC ) model [27]is applied to study and compare the production of H( H) cluster in these two isobaric collision systems. Pre-vious works of (anti-)nuclei and (anti-)hypernuclei pro-duction for different collision systems, e.g., pp [27–29],Cu+Cu [20, 30], Au+Au [31–34] and Pb+Pb [35, 36]interactions, have been studied in high energy region us-ing the same framework. In this study, we expect toexplore and investigate the production and propertiesof H ( H) in collision systems involving medium-heavynucleus.The paper is organized as follows: In sect. II, weprovide a concise introduction to the
PACIAE and
DCPC model. Sec. III contains our numerical calculations forproduction and properties of H ( H). In sec. IV, wesummarize our results.
II. MODELS
The
PACIAE model [26] is based on
PYTHIA
N N ) collisions ac-cording to the collision geometry and
N N total crosssection. The strings created in the
N N collisions willbreak up into free partons leading to the formation ofthe deconfined quark-gluon matter (QGM). After that,the decomposed partons interact with each other re-lied on the 2 → K factor is added to account for non-perturbative QCD and higher-order corrections. Then,the hadronization conducts via either the Lund stringfragmentation model [37] or the phenomenological coa-lescence model [26]. The last step is the hadron rescat-tering process happening among the generated hadronsuntil the hadronic freeze-out. (For more details seeRef. [26]).The DCPC model [27] is developed to calculate pro-duction of light (anti-)nuclei and (anti-)hypernuclei, af-ter the final-state particles have been produced in highenergy collisions. According to the quantum statisticalmechanics, one can estimate the yield of a single particlein the six-dimension phase space by an integral Y = Z H E d~qd~ph , (1)where H and E represent the Hamiltonian and energyof the particle, respectively. Similarly, the yield of Nparticle cluster can also be computed using the followingintegral Y N = Z ... Z H E d~q d~p ...d~q N d~p N h N . (2)In addition, equation (2) must meet the following con-straint conditions m m inv m + ∆ m, (3) | ~q ij | D , ( i = j ; i, j = 1 , , . . . , N ) . (4)where m inv = "(cid:18) N X i =1 E i (cid:19) − (cid:18) N X i =1 ~p i (cid:19) / , (5)and E i , ~p i ( i =1,2,. . . , N ) are the energies and momenta ofparticles, respectively. m and D denote the rest massand diameter of light (anti-)nuclei or (anti-)hypernuclei.Here, the values R = 1.74, 1.61, 5.0 fm are chosen forthe radius of He ( He), H ( H), and H ( H) in thissimulation, respectively [19, 21, 39]. ∆ m representsthe allowed mass uncertainty, and | ~q ij | presents the dis-tance between particles i -th and j -th. The integration inEq. (2) should be replaced by the summation over dis-crete distributions, as a coarse graining process in thetransport model. III. RESULTS AND DISCUSSION
At first, we can obtain the final state particles in cen-tral collisions of isobaric Ru+Ru and Zr+Zr using the
PACIAE model. This simulation works on the assump-tion that (anti-)hyperons heavier than Λ (Λ) have al-ready decayed, and the model parameters are fixed onthe default values given in
PYTHIA model, except the K factor and string fragmentation parameters parj(1),parj(2), and parj(3). These selected parameters are con-firmed by roughly fitting production of p ( p ) and Λ (Λ)in 0-15% Ru+
Ru and
Zr+
Zr collisions to STARdata in 20-40% centrality Au+Au collisions at √ s NN =200 GeV, since their mean number of participating nu-cleons ( h N part i ) are quite similar ∼ dN/dy ) of p and p with | η | < . < p T < . | η | < . < p T < . p and p take into account of contributionsfrom primordial Λ decays. For comparison, the STARexperimental data of 20-40% Au+Au collisions [40, 41]are also presented. It can be seen from Tab. I that theyields of particles ( p , p , Λ, and Λ) in Ru+
Ru collisionare the same as those of
Zr+
Zr collisions at the spec-ified collision centrality. Moreover, the
PACIAE model re-sults for the two isobaric nuclear collisions are well con-sistent with the measured STAR data for Au+Au colli-sions. The same fitted parameters of K = 3.0, parj(1) =0.13, parj(2) = 0.65, and parj(3) = 0.44 are chosen forthese two isobaric nuclear collision systems. TABLE I: The integrated yield dN/dy of particles ( p , p , Λand Λ) in 0-15% centrality Ru+
Ru and
Zr+
Zr colli-sions of √ s NN = 200 GeV, as compared to 20-40% Au+Aucollisions in STAR experimental data [40, 41]. Here p ( p ) areinclusive of contributions from primordial Λ (Λ) decays.Particle PACIAE
STARtype Ru+Ru(0-15%) Zr+Zr(0-15%) Au+Au(20-40%) h N part i . ± . . ± . ± p ± ± ± p ± ± ± ± ± ± ± ± ± Figure 1(a) presents the transverse momentum distri-butions of p ( p ) and Λ (Λ) (open symbols) in 0-15% Ru+
Ru and
Zr+
Zr collisions at √ s NN = 200GeV calculated by the PACIAE model. The STAR ex-perimental data for 20-40% Au+Au collisions taken fromRefs. [40, 41] are shown by the solid symbols. It can beseen that the transverse momentum spectrum of parti-cles p ( p ) and Λ (Λ) simulated by PACIAE model are com-patible with the STAR data within uncertainties. Be-sides, Figure 1(b) shows the distribution of the invariantyield ratios of particles for
Ru+
Ru and
Zr+
Zrcollisions at √ s NN = 200 GeV, as a function of p T . Ob- -6 -5 -4 -3 -2 -1 A+A coll. 200 GeV pp x STAR data
Zr+Zr, 0-15%Ru+Ru, 0-15% Au+Au, 20-40% d N / ( T dp T d y ) (( G e V ) - c ) p T (GeV/c) PACIAE model (a)(b) pp Z r + Z r / R u + R u r a t i o ratio = 1 FIG. 1: (a) The transverse momentum spectrum of parti-cles ( p , p , Λ, Λ) in midrapidity Ru+
Ru and
Zr+
Zrcollisions at √ s NN = 200 GeV. The open symbols show theresults of PACIAE model, and the solid symbols show the re-sults from STAR data [40, 41]. For clarity the spectra dataare divided by powers of 10. (b) The yield ratios of parti-cles ( p , p , Λ, Λ) produced in Ru+
Ru collisions to that in
Zr+
Zr collisions. viously, one can see from Figure 1(b) that there is nosignificant difference for transverse momentum spectraof (anti-)particles between the two isobaric nuclear col-lisions, except the fluctuation at higher p T .In the following, we generate 4 . × most central(0-10%) events for Ru+
Ru and
Zr+
Zr collisionsat √ s NN = 200 GeV with the PACIAE model, respec-tively. These (anti-)nucleons and (anti-)hyperons pro-duced within
PACIAE are used as input for the
DCPC model. The proton productions from Λ feed down con-tribution is excluded in the coalescence procedure. Then,we obtain the integrated yields dN/dy of (anti-)light(anti-)nuclei and (anti-)hypertriton nuclei with | η | < . p T < . m = 1 . H ( H), and ∆ m = 2 .
13 MeV for He ( He)and H ( H).Table II presents the integrated yields dN/dy of(anti-)hyperons and (anti-)hypertriton (Λ , Λ, H, H),as well as (anti-)nuclei ( p, p , He , He , H , H) calcu-lated by the
PACIAE+DCPC model in most central (0- 10%)
Ru+
Ru and
Zr+
Zr collisions at √ s NN =200 GeV, respectively. It can be seen that the yieldsof (anti-)hypertriton, (anti-)tritium, and (anti-)helium-3 nuclei in central Ru+
Ru and
Zr+
Zr collisionsat √ s NN = 200 GeV from the PACIAE+DCPC simula-tions, are all at the order of 10 − . However, the yieldsof (anti-)hypernuclei are less than that of correspond-ing (anti-)nuclei with the equal baryon numbers. Theyields of (anti-)hypernuclei and (anti-)nuclei in isobaric Ru+
Ru and
Zr+
Zr collisions are the same withinthe range of uncertainty.
TABLE II: The integrated yields dN/dy of (anti-)particles p ( p ), Λ (Λ), and (anti-)nuclei H ( H), He ( He), H ( H)calculated by
PACIAE+DCPC model in 0-10%
Ru+
Ruand
Zr+
Zr collisions of √ s NN = 200 GeV with | η | < . p ( p ) productions from Λ (Λ) feed down contribution isexcluded in the coalescence procedure.Nucleus type Ru+Ru(0-10%) Zr+Zr(0-10%) h N part i . ± . . ± . p ± ± p ± ± ± ± ± ± H (10 − ) 6.55 ± ± H (10 − ) 3.17 ± ± He (10 − ) 8.62 ± ± He (10 − ) 4.44 ± ± H (10 − ) 8.77 ± ± H (10 − ) 4.88 ± ± p He H R a t i o ( R u + R u / Z r + Z r ) A+A coll. 200 GeV, 0-10%
PACIAE+DCPC
Particle
Antiparticle H p He H H FIG. 2: The yield ratios of (anti-)hypernuclei and (anti-)nuclei in
Ru+
Ru collisions to that in
Zr+
Zr colli-sions at √ s NN = 200 GeV from the PACIAE+DCPC simula-tions.
To facilitate the comparison of the production of(anti-)nuclei and (anti-)hypernuclei between isobaricRu+Ru and Zr+Zr collision systems, the yield ratios
TABLE III: The (anti-)nucleus ratios from the
PACIAE+DCPC model in central (0-10%)
Ru+
Ru and
Zr+
Zr collisionsat √ s NN = 200 GeV. The top section of the table shows the three ratios of anti-nucleus to nucleus, followed by the mixedratios of (anti-)nucleus to (anti-)nucleus. The ratios between proton, anti-proton, hyperon, and anti-hyperon are shown at thebottom. STAR data are taken from Cu+Cu and Au+Au collisions at √ s NN = 200 GeV [6, 40–43], respectively.Ratio Cu+Cu(STAR) Au+Au(STAR) Ru+Ru( PACIAE+DCPC ) Zr+Zr(
PACIAE+DCPC ) H / H − . ± . ± .
07 0 . ± .
07 0 . ± . He / He 0 . ± .
17 0 . ± . ± .
04 0 . ± .
08 0 . ± . H / H − − . ± .
10 0 . ± . H / He − . ± . ± .
13 0 . ± .
08 0 . ± . H / He − . ± . ± .
12 0 . ± .
06 0 . ± . H / H − − . ± .
08 0 . ± . H / H − − . ± .
07 0 . ± . / p 0.80 ± ± . ± .
04 0 . ± . / Λ 0.82 ± ± . ± .
02 0 . ± . / p 0.84 ± − . ± .
03 0 . ± . / p 0.83 ± − . ± .
04 0 . ± . of (anti-)hypernuclei and (anti-)nuclei produced by PA-CIAE+DCPC model in Ru+Ru collisions to that in Zr+Zrcollisions are presented in Fig. 2. It is observed fromTab. II and Fig. 2 that the yield ratio values betweenthese two collision systems are all close to unity, i.e.,the productions of (anti-)hadrons and (anti-)nuclei showno difference in isobaric nuclear collision systems whentheir h N part i are the same, although these two collisionsystems have different proton numbers.In order to understand the fundamental properties ofantimatter in nuclear collisions, we provide a system-atic investigation to the yield ratios of different (anti-)nuclei and (anti-)hypernuclei, which are deeply relatedto the fractions of constituent nucleons in the naive coa-lescence framework [11, 15]. For instance, the yield ratioof H / H should be proportional to ( p/p )( n/n )(Λ / Λ),which is approximate to ( p/p ) (Λ / Λ), i.e, H H = pnΛpnΛ ≃ ( pp ) ΛΛ . (6)Table III represents the yield ratios of antiparti-cles to particles ( p/p , Λ / Λ, H / H, He / He, H / H),and the mixed ratios (Λ /p , Λ /p , H / He, H / He, H / H, H / H) calculated by
PACIAE+DCPC modelin
Ru+
Ru and
Zr+
Zr collisions at √ s NN =200 GeV. One can see from Table III that the yield ra-tios of H / H, He / He, and H / H are the same withinthe error range, although their yields are not the same asshown in Table II. And the ratio values of antiparticlesto particles and mixed ratio values of (anti-)particles to(anti-)particles in central isobaric Ru+Ru and Zr+Zr at √ s NN = 200 GeV, are the same in the range of uncer-tainty. The yield ratio results of antiparticles to parti-cles and their mixed ratios simulated by PACIAE+DCPC model are found to be in agreement with the above the-oretical interpretation within uncertainties.
Au+Au, 0-80%Au+Au, 20-40% He H H H R a t i o A+A coll. 200 GeV, 0-10%
PACIAE+DCPCSTAR
Cu+Cu, 0-10%
Ru+Ru Zr+Zr H p p He p p H H He He H H H H FIG. 3: The ratios and mixed ratios of (anti-)matter form
PACIAE+DCPC model(open symbols) in 0-10% Ru+Ru andZr+Zr collisions, compared with Cu+Cu and Au+Au colli-sions. The data are taken from STAR [6, 40–43]. The verticallines and error boxes show statistical and systematic errors,respectively.
Fig. 3 and Table III show that the ratios of anti-nucleito nuclei ( H / H, He / He, H / H) are less than 1,meaning that the yields of antiparticles is less than thatof corresponding particles; similarly, the mixed ratio val-ues indicate that the yields of the (anti-)hypertriton areless than that of (anti-)nuclei. Our simulation results areconsistent with the STAR data of Cu+Cu [41–43] andAu+Au [6, 40, 41] collisions at √ s NN = 200 GeV.In nuclear collisions, the invariant yields for produc-
100 150 200 250 300 35010 -6 -5 -4 -3 -2 -1 STAR Au+Au, 0-12%
PACIAE+DCPC B ( G e V / c )
FIG. 4: Coalescence parameters √ B of (anti-)hypertritonand light (anti-)nuclei in central A+A collisions, as a functionof N part . The open symbols denote our results evaluated by PACIAE+DCPC . The solid points take from STAR [44] andALICE [7]. The error bars show statistical uncertainties. tion of (anti-)hypernuclei and (anti-)nuclei can be relatedto the primordial yields of (anti-)nucleons in the coales-cence framework [45, 46] by Eq. (7) E A d N A d P A ≈ B A ( E P d N P d P P ) A , (7)where Ed N/d p stands for the invariant yields of nucle-ons or light (anti-)nuclei and (anti-)hypernuclei, and A is the atomic mass number, respectively. B A representsthe coalescence parameters, which relates to the freeze-out correlation volume, i.e., B A ∝ V − Af . p A , p p denotetheir momentum, with p A = Ap p assumed.Fig. 4 presents coalescence parameters √ B of H( H), He ( He), and H ( H), as a function of N part in Ru+Ru and Zr+Zr collisions, as well as Cu+Cu [20],Au+Au [34], and Pb+Pb [35] collisions, respectively.One can see that √ B calculated by PACIAE+DCPC model gradually decrease with the increasing N part indifferent A+A collision systems, indicating that the cor-relation volume for π ± HBT at thermal freeze-out be-comes larger [34, 44]. Specifically, with respect to 0-10%Ru+Ru or Zr+Zr collisions, the values of √ B for nu-clei H, He, H and their corresponding anti-nuclei H, He, H are about 3 . × − , 3 . × − , 3 . × − and 3 . × − , 3 . × − , 3 . × − , respectively.It is clear that the value of √ B of (anti-)hypertriton issmaller than that of (anti-)nuclei although their atomicmass number are same, suggesting that there exists anadditional penalty factor due to strangeness [15, 35].One can also find that the negative (hyper-)nuclei are slightly smaller than that of positive (hyper-)nuclei.Meanwhile, the experiment data of 0-12% Au+Au inSTAR [44] and 0-10% Pb+Pb from ALICE [7] are alsopresented in Fig. 4.
100 150 200 250 300 3500.00.51.01.52.0 s t3 s t3 s s s s s PbPbAuAuRuRu(ZrZr)
PACIAE+DCPC S ( S t )
STAR Au+Au, 0-80%STAR Au+Au, 0-80%ALICE Pb+Pb, 2.76TeVALICE Pb+Pb, 2.76TeVCuCu s FIG. 5: Comparison of strangeness population factor s ( s t )in different A+A collisions. The open symbols denote theresults computed by PACIAE+DCPC , and the solid pointsdenote data from STAR [6] and ALICE [7]. Error bars anderror boxes denote statistical and systematic errors, respec-tively.
The strangeness population factor s , should be aboutone in the coalescence model for particle production, asfirst suggested in Ref. [21]. It is a possible tool to studythe nature of a quark-gluon plasma created in high en-ergy nuclear collisions [47], due to its sensitivity to thelocal baryon-strangeness correlation [48, 49]. This factortypically is written as s = ( H × p) / ( He × Λ) , (8)which can be straightforwardly extended to H expressedas s t = ( H × p) / ( H × Λ) . (9)In the Fig. 5, we compares the values of s ( s ) and s t ( s t ) vary with N part calculated by PACIAE+DCPC model for different central A+A collisions, includ-ing Cu+Cu [20], Ru+Ru(Zr+Zr), Au+Au [34], andPb+Pb [35] collision systems. It is shown that the valuesof s ( s ) and s t ( s t ) for three-body coalescence slightlydecrease as N part increases from 100 to 360 in central(0-10%) Cu+Cu, Ru+Ru(Zr+Zr), Au+Au, and Pb+Pbcollisions. Numerically, the present values of s , s and s t , s t are 0 . ± . , . ± .
15 and 0 . ± . , . ± . . ± . , . ± . . ± . , . ± .
09 in 0-10% Zr+Zr collisions,respectively. Meanwhile, the values of s ( s ) and s t ( s t )shown in the Fig. 5 for Au+Au and Pb+Pb collisions cal-culated by PACIAE+DCPC model are in agreement withthe corresponding data from STAR [6] and ALICE [7]within uncertainties.
IV. CONCLUSION
In this paper, we use the
PACIAE+DCPC model to sim-ulate production of H and H, as well as H, H, He,and He in isobaric
Ru+
Ru and
Zr+
Zr centralcollisions at √ s NN = 200 GeV with | η | < . p T < H , H) and (anti-)nuclei( H, H, He , He) in isobaric Ru+Ru and Zr+Zr col-lisions. It is found that there is no difference in thegeneration and properties of (anti-)matter ( H , H, H, H, He , He) in isobaric Ru+Ru and Zr+Zr collisionsystems. Then the yield of (anti-)hypertriton ( H , H)is less than that of light (anti-)nuclei ( H, He, H, He),which may be understood as the number of hyperons isless than that of nucleons in isobaric Ru+Ru and Zr+Zrcollision. However, the yields ratio ( H / H, He / He, H / H) and the mixed ratios ( H / He, H / He, H / H, H / H), coalescence parameters √ B and strangenesspopulation factor s of (anti-)hypertriton and light (anti-)nuclei are all the same within uncertainty.In addition, the experimental data of Cu+Cu, Au+Auand Pb+Pb collisions from RHIC, ALICE are includedin the comparison. The results show that the coales-cence parameters √ B of H ( H), He ( He), H ( H)and the strangeness population factor s ( s t ) slightly de-crease with the increasing N part in different central A+Acollision systems, including Cu+Cu, Ru+Ru/Zr+Zr toAu+Au and Pb+Pb collisions.The productions of H ( H), He ( He), H ( H) clus-ter in isobaric
Ru+
Ru and
Zr+
Zr collisions at √ s NN = 200 GeV are predicted with the theoreticalmodel. Thus we expect that the upcoming experimentalmeasurement at RHIC-STAR would be used to testifyour predictions on H ( H) production presented in thiswork. ACKNOWLEDGMENTThis work was supported by NSFC(11475149, 11775094,11905188), as well as supported by the high-performancecomputing platform of China University of Geosciences.The authors thank Fengxian Liu and Zijian Dong forfruitful discussions. [1] J.H. Chen, D. Keane, Y.G. Ma et al. , Phys. Rep. ,1(2018).[2] Y.G. Ma, J.H. Chen, and L. Xue, Front. Phys. , 637(2012).[3] J. Adam et al. , (ALICE Collaboration), Nat. Phys. ,811(2015).[4] J. Adam et al , (STAR Collaboration), Nat. Phys. ,409(2020).[5] S. Acharya et al , (ALICE Collaboration), Phys. Lett. B , 134905(2019).[6] B.I. Abelev et al. , (STAR Collaboration), Science ,58(2010).[7] J. Adam et al. , (ALICE Collaboration), Phys. Lett. B , 360(2016).[8] E. Botta, T. Bressani, and G. Garbarino, Eur. Phys. J.A , 41(2012).[9] V. Topor Pop and S. Das Gupta, Phys. Rev. C ,054911(2010).[10] A. Andronic, P. Braun-Munzinger, J. Stachel et al. ,Phys. Lett. B , 203(2011).[11] J. Cleymans, S. Kabana, I. Kraus et al. , Phys. Rev. C , 054916(2011).[12] S. Pal and W. Greiner, Phys. Rev. C , 054905 (2013).[13] S. Chatterjee and B. Mohanty, Phys. Rev. C , 034908(2014).[14] A. Andronic, P. Braun-Munzinger, K. Redlich et al. , Na-ture , 321(2018).[15] L. Xue, Y.G. Ma, J. H. Chen et al. , Phys. Rev. C , 064912(2012).[16] L.L. Zhu, C. M. Ko, and X.J. Yin, Phys. Rev. C ,064911(2015).[17] N. Shah, Y.G. Ma, J.H. Chen et al. , Phys. Lett. B ,6(2016).[18] K.J. Sun and L.W. Chen, Phys. Rev. C , 064909(2016).[19] P. Liu, J.H. Chen, Y.G. Ma, and S. Zhang, Nucl. Sci.Technol. , 55(2017).[20] F.X. Liu, G. Chen, Z.L. She et al, Phys. Rev. C ,034904(2019).[21] T. Armstrong et al. , (E864 Collaboration), Phys. Rev.C , 024902(2004).[22] Y.F. Sun and C.M. Ko, Phys. Rev. C , 014911(2018).[23] H.J. Xu, X.B. Wang, H.L. Li et al. , Phys. Rev. Lett. , 022301(2018).[24] X.L. Zhao, G.L. Ma and Y.G. Ma, Phys. Rev. C ,034903(2019).[25] J. Adam et al. , (STAR collaboration), arXiv:1911.00596.[26] B.H. Sa, D.M. Zhou, Y.L. Yan et al. , Comput. Phys.Commun. , 333(2012).[27] Y. L. Yan, G. Chen, X. M. Li et al. , Phys. Rev. C ,024907(2012).[28] J.L. Wang, D.K. Li, H.J. Li et al. , Int. J. Mod. Phys. E (12),1450088(2014).[29] N.A. Ragab, Z.L. She and G. Chen, arXiv:1911.11919.[30] F.X. Liu, G. Chen, Z.L. She et al. , Eur. Phys. J. A (9),160(2019). [31] G. Chen, Y.L. Yan, D.S. Li et al. , Phys. Rev. C ,054910 (2012).[32] G. Chen, H. Chen, J. Wu et al. , Phys. Rev. C , 034908(2013).[33] G. Chen, H. Chen, J.L. Wang et al. , J. Phys. G: Nucl.Part. Phys. , 115102(2014).[34] Z.J. Dong, Q.Y. Wang, G. Chen et al. , Eur. Phys. J. A , 144(2018).[35] Z.L. She, G. Chen, H.G. Xu et al. , Eur. Phys. J. A ,93(2016).[36] Z.L. She, G. Chen, D.M. Zhou et al. , arXiv:1909.07070.[37] T. Sj¨ostrand, S. Mrenna, and P. Skands, J. High EnergyPhys. , 026(2006).[38] B.L. Combridge, J. Kripfgang, and J. Ranft, Phys. Lett.B , 234(1977).[39] H. Nemura, Y. Suzuki, Y. Fujiwara et al. , Prog. Theor.Phys. , 929(2000).[40] B.I. Abelev et al. , (STAR Collaboration), Phys. Rev. C , 034909(2009). [41] G. Agakishiev et al. , (STAR Collaboration), Phys. Rev.Lett. , 072301(2012).[42] M. M. Aggarwal et al. , (STAR Collaboration), Phys.Rev. C , 034910(2011).[43] J. Zhou, Light (anti-)nuclei production in the STAR ex-periment at RHIC, Ph.D. thesis, Rice University, 2009(unpublished).[44] B. I. Abelev et al. ,(STAR collaboration), arXiv:0909.0566.[45] R. Scheibl, U. Heinz, Phys. Rev. C , 1585(1999).[46] H.H. Gutbrod, A. Sandoval, P.J. Johansen et al. , Phys.Rev. Lett. , 667(1976).[47] S. Zhang, J.H. Chen, H. Crawford et al. , Phys. Lett. B , 224(2010).[48] V. Koch, A. Majumder, J. Randrup, Phys. Rev. Lett. , 182301(2005).[49] J. Steinheimer, K. Gudima, A. Botvina et al. , Phys. Lett.B714