核子聚并模型是高能重离子碰撞中轻核产生最常用的理论模型之一。本文利用输运模型JAM结合简化的后处理聚并模块，研究了质心系能量$\u221as_{NN}=3$ GeV的Au+Au碰撞中轻核$d$、$t$、$^{3}$He和$^{4}$He的产生过程。我们扫描了核子聚并形成轻核的唯象聚并参数截断值，即相对空间距离$ΔR$和动量差$ΔP$，以重现STAR实验测量的轻核$p_{\ m T}$谱。结果表明，聚并参数与这些轻核的结合能以及直径之间存在潜在关联。
英文摘要：
The nucleon coalescence model is one of the most popular theoretical models for light nuclei production in high-energy heavy-ion collisions. The production of light nuclei $d$, $t$, $^{3}$He, and $^{4}$He is studied using the transport model JAM with a simplified afterburner coalescence at $\sqrt{s_{NN}}=3$ GeV Au+Au collisions. We scan the cut-off of phenomenological coalescence parameters, the relative spatial distance $ΔR$ and momentum difference $ΔP$, for formation of light nuclei by nucleon coalescence to reproduce the light nuclei $p_{\rm T}$ spectra measured by STAR experiment. The results indicate a potential connection between the coalescence parameters and the binding energy as well as the diameter of these light nuclei.
The directed flow ($v_{1}$) of open charm meson ($D^{0}$) is studied in Au+Au collisions at $\sqrt{s_{NN}}$ = 200~GeV using A Multi-Phase Transport (AMPT) model framework with partonic interactions (string melting version). Within this framework, it is found that although the initial spatial eccentricity ($ε_{1}$) of charm quark is smaller than light quarks, the charm quark $v_{1}$ magnitude is found to be approximately 7 times larger than that of the light u quark at large rapidity. This indicates that the charm quarks can retain more information from initial condition than the light quarks. …
The thermal model properly describes the production yields of light nuclei in relativistic heavy-ion collisions even so the loosely bound sizable nuclei cannot exist in the dense and hot hadron gas at a chemical freeze-out. Within the coalescence model, light nuclei are formed at the latest stage of nuclear collisions - a kinetic freeze-out - due to final state interactions. After discussing the models, we derive simple analytic formulas and, using model parameters directly inferred from experimental data, we show that the thermal and coalescence model predictions are quantitatively close to e…
Light (anti-)nuclei in relativistic heavy-ion collisions are considered to be formed by the coalescence mechanism of (anti-)nucleons in the present work. Using a dynamical phase-space coalescence model coupled with a multi-phase transport (AMPT) model, we explore the formation of light clusters such as deuteron, triton and their anti-particles in different centralities for $^{197}$Au + $^{197}$Au collisions at $\sqrt{s_{NN}} = 39$ GeV. The calculated transverse momentum spectra of protons, deuterons, and tritons are comparable to those of experimental data from the RHIC-STAR collaboration. Bot…
We present results of a phase space coalescence approach within the UrQMD transport and -hybrid model for a very wide range of beam energies from SIS to LHC. The coalescence model is able to qualitatively describe the whole range of experimental data with a fixed set of parameters. Some systematic deviations are observed for very low beam energies where the role of feed down from heavier nuclei and multi-fragmentation becomes relevant. The coalescence results are mostly very close to the thermal model fits. However, both the coalescence approach as well as thermal fits are struggling to simult…
The production of light nuclei in relativistic heavy-ion collisions is well described by both the thermal model, where light nuclei are in equilibrium with hadrons of all species present in a fireball, and by the coalescence model, where light nuclei are formed due to final-state interactions after the fireball decays. We present and critically discuss the two models and further on we consider two proposals to falsify one of the models. The first proposal is to measure a yield of exotic nuclide $^4{\rm Li}$ and compare it to that of $^4{\rm He}$. The ratio of yields of the nuclides is quite di…
With the kinetic freeze-out nucleons and antinucleons obtained from the quark combination model, we study the production of light nuclei and antinuclei in the (anti-)nucleon coalescence mechanism in relativistic heavy ion collisions. We derive analytic formulas of the momentum distributions of different light nuclei and apply them to compute transverse momentum ($p_T$) spectra of (anti-)deuterons ($d$, $\bar d$) and (anti-)tritons ($t$, $\bar t$) in Au-Au collisions at $\sqrt{s_{NN}}=$7.7, 11.5, 19.6, 27, 39, 54.4 GeV. We find that the experimental data available for these $p_T$ spectra can be…
We present a detailed comparison of coalescence and thermal-statistical models for the production of (anti-)(hyper-)nuclei in high-energy collisions. For the first time, such a study is carried out as a function of the size of the object relative to the size of the particle emitting source. Our study reveals large differences between the two scenarios for the production of objects with extended wave-functions. While both models give similar predictions and show similar agreement with experimental data for (anti-)deuterons and (anti-)3He nuclei, they largely differ in their description of (anti…
The formation of light nuclei can be described as the coalescence of clusters of nucleons into nuclei. In the case of small interacting systems, such as dark matter and $e^+e^-$ annihilations or $pp$ collisions, the coalescence condition is often imposed only in momentum space and hence the size of the interaction region is neglected. On the other hand, in most coalescence models used for heavy ion collisions, the coalescence probability is controlled mainly by the size of the interaction region, while two-nucleon momentum correlations are either neglected or treated as collective flow. Recent…
The origin of weakly-bound nuclear clusters in hadronic collisions is a key question to be addressed by heavy-ion collision (HIC) experiments. The measured yields of clusters are approximately consistent with expectations from phenomenological statistical hadronisation models (SHMs), but a theoretical understanding of the dynamics of cluster formation prior to kinetic freeze out is lacking. The competing model is nuclear coalescence, which attributes cluster formation to the effect of final state interactions (FSI) during the propagation of the nuclei from kinetic freeze out to the observer. T…
A data-driven idea is presented to test if light nuclei and hypernuclei obey the coalescence-inspired sum rule, i.e., to test if the flow of a light nucleus or hypernucleus is the summed flow of each of its constituents. Here, the mass difference and charge difference among the constituents of light nuclei and hypernuclei are treated appropriately. The idea is applied to the available data for $\sqrt{s_{NN}} = 3$ GeV fixed-target Au+Au collisions at the Relativistic Heavy Ion Collider (RHIC), published by the STAR collaboration. It is found that the sum rule for light nuclei is approximately v…
Directed and elliptic flow of light nuclei and hypernuclei in Au+Au collisions at $\sqrt{s_\mathrm{NN}}=3$ GeV: Coalescence vs. Statistical Fragmentation
Sequential Clusterization of Light Nuclei and Hypernuclei in Heavy-Ion Collisions within a Wigner Function Coalescence Framework
Central China Normal University（华中师范大学）；University of Heidelberg（海德堡大学）；Johann Wolfgang Goethe University（约翰·沃尔夫冈·歌德大学）；GSI Helmholtz Center for Heavy Ion Research（GSI亥姆霍兹重离子研究中心）
We study the production of $ΛΛ$ and $\overline{Λ\text{n}}$ exotic states in central Pb+Pb collisions at $\sqrt{s_{NN}}=2.76$ TeV at LHC via both hadron and quark coalescence within a covariant coalescence model with a blast-wave-like parametrization for the phase-space configurations of constituent particles at freezeout. In the hadron coalescence, the two states are considered as molecular states while they are considered as six-quark states in the quark coalescence.For $\overline{Λ\text{n}}$, we find that the yields of both molecular and six-quark states are much larger than the experimental…
Using the coalescence model based on the phase-space distributions of protons, neutrons, Lambdas and their antiparticles from a multiphase transport (AMPT) model, we study the production of deuteron, triton, helium 3, hypertriton, hyperhelium 3 and their antinuclei in Pb+Pb collisions at $\sqrt{s_{NN}}=2.76$ TeV. The resulting transverse momentum spectra, elliptic flows and coalescence parameters for these nuclei are presented and compared with available experimental data. We also show the constituent number scaled elliptic flows of these nuclei and discuss their implications.
Transverse momentum spectra of pions, protons and antiprotons in Au+Au collisions at intermediate RHIC energy of $\sqrt{s_{NN}}=62$ GeV are studied in a model that includes both quark coalescence from the dense partonic matter and fragmentation of the quenched perturbative minijet partons. The resulting baryon to meson ratio at intermediate transverse momenta is predicted to be larger than that seen in experiments at higher center of mass energies.
Technical University of Munich（慕尼黑工业大学）；Thomas Jefferson National Accelerator Facility（托马斯·杰斐逊国家加速器设施）；INFN Pisa（意大利国家核物理研究所比萨分部）；Università di Bologna（博洛尼亚大学）；Università di Pisa（比萨大学）
The energy dependence of light (anti)nuclei and (anti)hypertriton production are investigated in central Au-Au collisions from AGS up to LHC energies at midrapidity, using the parton and hadron cascade model (PACIAE) together with the dynamically constrained phase-space coalescence model(DCPC). We find that the yields, yield ratios of the antiparticles to their corresponding particles, the coalescence parameters $B_A$ and the strangeness population factor $s_3$ of light (anti)nuclei and (anti)hypertriton strongly depend on the energy. Furthermore, we analyze and discuss the strangeness populat…
The number of constituent quarks (NCQ-) scaling of hadrons and the number of constituent nucleons (NCN-) scaling of light nuclei are proposed for nuclear modification factors ($R_{cp}$) of hadrons and light nuclei, respectively, according to the experimental investigations in relativistic heavy-ion collisions. Based on coalescence mechanism the scalings are performed for pions and protons in quark level, and light nuclei $d (\bar d)$ and $^3$He for nucleonic level, respectively, formed in Au + Au and Pb + Pb collisions and nice scaling behaviour emerges. NCQ or NCN scaling law of $R_{cp}$ can …
We show that coalescence of nucleons emitted prior to thermalization in highly excited nuclei can explain the anomaly of kinetic energies of helium clusters. A new coalescence algorithm has been included into the statistical approach to nuclear reactions formerly used to describe intermediate mass fragment production.
We investigate the collision energy dependence of deuteron and antideuteron emission in the RHIC-BES low- to mid-energy range $\sqrt{s_{NN}} = 4.6-200$ GeV where the formation rate of antinuclei compared to nuclei is strongly suppressed. In the coalescence picture, this can be understood as bulk emission for nuclei in contrast to surface emission for antinuclei. By comparison with experimental data on the coalescence parameter $B_2$, we are able to extract the respective source geometries. This interpretation is further supported by results from the UrQMD transport model, and establishes the f…
We investigate the coalescence factors $B_2$ and $B_3$ at low collision energies ($\sqrt{s_\mathrm{NN}}<6$ GeV) with special focus on the HADES and RHIC-BES experiments. It is shown that, in order to properly interpret the coalescence factors $B_A$, two important corrections are necessary: I) $B_2$ has to be calculated using the proton $\times$ neutron yields in the denominator, instead of the square of the proton yield, and II) the primordial proton (neutron) densities have to be used for the normalization and not the final state (free) protons (neutrons). Both effects lead to a drastic reduc…
We have used the dynamically constrained phase space coalescence model to investigate the centrality dependence of light (anti)nuclei and (anti)hypertriton production based on the $6.2\times 10^7$ hadronic final states generated by the PACIAE model in Au+Au collisions at $\sqrt{s_{\rm{NN}}}=200$ GeV in $|y| <1$ and $p_T<5$ acceptances. It turned out that the yields of light (anti)nuclei and (anti)hypertriton strongly depend on the centrality, i.e. their yields decrease rapidly with the increase of centrality bins; but their yield ratios are independent on centrality. These theoretical results …
We study the momentum dependence of the production of light nuclei in high energy collisions in the nucleon coalescence/recombination mechanism. We derive formulas of the momentum distributions of deuterons ($d$) and helions ($^3$He). We obtain the analytic expressions of the coalescence factor $B_A$'s ($B_2$ for $d$ and $B_3$ for $^3$He) as functions of the collision system size and the momentum. We apply the deduced results to p-p, p-Pb and Pb-Pb collisions to naturally explain the interesting behaviors of $B_A$ observed in experiments at the CERN Large Hadron Collider.
We investigate the properties of light (anti)nuclei and (anti)hypertriton production in Pb-Pb collisions at $\sqrt{s_{\rm{NN}}}=2.76$ TeV, based on the parton and hadron cascade and dynamically constrained phase-space coalescence (PACIAE + DCPC) model. We found that the yields of light (anti)nuclei and (anti)hypertriton strongly depend on the centrality, i.e., their yields decrease rapidly with the increase of centrality bins, but their yield ratios are independent of centrality. The results of theoretical model are well consistent with ALICE data. Furthermore, we found that the integrated yie…
Elliptic flow of hadrons observed at relativistic heavy-ion collision experiments at Relativistic Heavy-Ion Collider (RHIC) and Large Hadron Collider (LHC), provides us an important signature of possible de-confinement transition from hadronic phase to partonic phase. However, hadronization processes of de-confined partons back into final hadrons are found to play a vital role in the observed hadronic flow. In the present work, we use coalescence mechanism also known as Recombination (ReCo) to combine quarks into hadrons. To get there, we have used Boltzmann transport equation in relaxation ti…
The production of light (anti)nuclei have been investigated using the dynamically constrained phase-space coalescence model based on the final-state hadrons generated by the PACIAE model in Cu+Cu collisions at $\sqrt{s_{\rm{NN}}}=200$GeV with $|η|<0.5$ and $0<p_T<8$GeV/c. The results show that there is a strong centrality dependence of yields of $\rm d$, $\rm\overline d$, $\rm ^3He$, $\rm^3\overline {He}$, $\rm ^4He$, and $\rm^4\overline {He}$, i.e., their yields decrease rapidly with the increase of centrality, and the greater the mass is, the greater the dependence shows; whereas their ratio…
Fragmentation reactions induced on light and medium nuclei by protons and light nuclei of energies around 1 GeV/nucleon and below are studied with the Los Alamos transport code MCNP6 and with its CEM03.03 and LAQGSM03.03 event generators. CEM and LAQGSM assume that intermediate-energy fragmentation reactions on light nuclei occur generally in two stages. The first stage is the intranuclear cascade (INC), followed by the second, Fermi breakup disintegration of light excited residual nuclei produced after the INC. CEM and LAQGSM account also for coalescence of light fragments (complex particles)…
Using a covariant quark coalescence model combined with a blast-wave-like analytical parametrization for (anti-)strange quark phase-space freeze-out configuration, we extract information on strange quark freeze-out dynamics in Pb+Pb collisions at $\sqrt{s_{NN}}$=2.76 TeV by fitting the measured transverse momentum spectra and elliptic flows ($v_2$) of $ϕ$ mesons and $Ω$ baryons. We find that although both the measured and calculated $v_2$ of $ϕ$ and $Ω$ satisfy the number-of-constituent-quark (NCQ) scaling, the NCQ-scaled $v_2$ is significantly smaller than the $v_2$ of strange quarks, implyin…
We study the production of charmed hadrons $D^{0}$ and $Λ_c^+$ in relativistic heavy-ion collisions using an improved quark coalescence model. In particular, we extend the usual coalescence model by letting a produced hadron to have the same velocity as the center-of-mass velocity of coalesced constituent quarks during hadronization to take into account the effect of collective flow in produced quark-gluon plasma. This results in a shift of charmed resonances of higher masses to larger transverse momenta ($p_T^{}$). Requiring all charm quarks of very low $p_T^{}$ to be converted to hadrons via…
We present an update of the event generator based on the three-fluid dynamics (3FD), complemented by Ultra-relativistic Quantum Molecular Dynamics (UrQMD) for the late stage of the nuclear collision~-- the three-fluid Hydrodynamics-based Event Simulator Extended by UrQMD final State interactions (THESEUS). Two modifications are introduced. The THESEUS table of hadronic resonances is made consistent with that of the underlying 3FD model. The main modification is that the generator is extended to simulate the light-nuclei production in relativistic heavy-ion collisions, on the equal basis with h…
We use the parton and hadron cascade (PACIAE) model and the dynamically constrained phase-space coalescence (DCPC) model to investigate the productions of (anti)hypertriton and light (anti)nuclei generated by 0-10% centrality $^{12}$C+$^{12}$C, $^{24}$Mg+$^{24}$Mg, $^{40}$Ca+$^{40}$Ca, and $^{64}$Cu+$^{64}$Cu collisions at $\sqrt{S_{NN}}$ = 200 GeV with $|y|$ $<$ 1.5 and $p_{T}$ $<$ 5. We study the yield ratios of the antiparticle to particle and the rapidity distributions of the different (anti)nuclei. We find that the amounts of antimatter produced are significantly lower than that of the co…
We present the production of light (anti)nuclei, (anti)hypertriton and di-Lambda based on coalescence model in central Au+Au collisions at $\sqrt{s_{NN}}=200GeV$. The invariant yields of \He(\Hebar), \hypert(\hypertbar), \Hee(\Heebar) obtained is found to be consistent with the STAR measurements. The $p_{T}$ integrated yields for di-Lambda $dN_{ΛΛ}/dy \sim 2.23\times10^{-5}$, and is not strongly dependent on the parameter employed for coalescence process. Relative particle ratios of light anti(nuclei) and (anti)hypertriton are explored, and agree with experimental data and thermal model predic…
We investigate the role of partonic degrees of freedom in high multiplicity p-Pb collisions at $\sqrt{s_{NN}}=$ 5.02 TeV carried out at the Large Hadron Collider (LHC) by studying the production and collective flow of identified hadrons at intermediate $p_T$ via the coalescence of soft and hard partons generated from viscous hydrodynamics (VISH2+1) and the energy loss model (LBT), respectively. We find that combining the intermediate $p_T$ hadrons from the coalescence with the low $p_T$ hadrons from hydrodynamics and high $p_T$ hadrons from the jet fragmentation, our Hydro-Coal-Frag model prov…
Light nuclei production is sensitive to the baryon density fluctuations and can be used to probe the QCD phase transition in relativistic heavy-ion collisions. In this work, we studied the production of proton, deuteron, triton in central Au+Au collisions at $\sqrt{s_{\mathrm{NN}}}$ = 5, 7.7, 11.5, 14.5, 19.6, 27, 39, 54.4, 62.4 and 200 GeV from a transport model (JAM). Based on the coalescence production of light nuclei, we calculated the energy dependence of rapidity density $dN/dy$ and particle ratios ($d/p$, $t/p$, and $t/d$). More importantly, the yield ratio $N_{t} \times N_{p} / N_{d}^{…
Baryon-strangeness correlation (C$_{BS}$) has been investigated with a multi-phase transport model (AMPT) in $^{197}$Au + $^{197}$Au collisions at $\sqrt{s_{NN}}$ = 200 GeV. The centrality dependence of C$_{BS}$ is presented within the model, from partonic phase to hadronic matter. We find that the system still reserve partial predicted signatures of C$_{BS}$ after parton coalescence. But after hadronic rescattering, the predicted signatures will be obliterated completely. So it seems that both coalescence hadronization process and hadronic rescattering are responsible for the disappearance of…
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 $Δr$ of the coalescence procedure as well as canonical effects. On the other hand, the double ratio $S_3$ is almost independent of canonical effects, which is in contrast to coalescence. Thus, both the beam energy dependence and cent…
Light nuclei and hyper-nuclei are produced in abundance in heavy-ion collisions. The production mechanism of these species in heavy-ion collisions still remains to be understood. In these proceedings, we report the transverse momentum and centrality dependence of elliptic flow ($v_2$) of $d$, $t$, and $^3\text{He}$ in Au+Au collisions at $\sqrt{s_{NN}}$ = 14.6, 19.6, 27, and 54.4 GeV. Mass number scaling of $v_2(p_T)$ of light nuclei is shown. We also report the first observation of hyper-nuclei $^{3}_Λ$H and $^{4}_Λ$H directed flow ($v_1$) in $\sqrt{s_{NN}}$ = 3 GeV mid-central (5-40\%) Au+Au…
We present the scaling properties of mass number of light (anti)nuclei production in midrapidity Au + Au collisions at $\sqrt {s_{NN}}=200$ GeV based on the PACIAE + DCPC model. It is found that the integrated yield of light (anti)nuclei decreased exponentially with the increase of mass numbers which depends on the centrality, this properties of the system can be described quantitatively by temperature $T$ at hadronic freeze-out, and the model results are consistent with STAR data. Furthermore, we found that the integrated yield of heavier (anti)nuclei per participant nucleon increases from pe…
The formation of deuterons in heavy-ion collisions at relativistic energies is investigated by employing two recently advanced models -- the Minimum Spanning Tree (MST) method and the coalescence model by embedding them in the PHQMD and the UrQMD transport approaches. While the coalescence mechanism combines nucleons into deuterons at the kinetic freeze-out hypersurface, the MST identifies the clusters during the different stages of time evolution. We find that both clustering procedures give very similar results for the deuteron observables in the UrQMD as well as in the PHQMD environment. Mo…
Using the coalescence model based on the phase-space distribution of nucleons from an extended blast-wave model that includes the space-momentum correlation of high momentum nucleons, we study the transverse momentum spectra and elliptic flows of deuteron and helium-3 in Pb+Pb collisions at the energy $\sqrt{s_{NN}}=2.76$ TeV. We find that the measured elliptic flows of deuteron can be satisfactorily described if nucleons of large transverse momenta are more spread in space when their momenta are more aligned along the reaction plane.
The production of $\rm{^3_ΛH}$ and $\rm{{^3_{\overline Λ}\overline H}}$, as well as $\rm{^3H}$, $\rm{^3\overline H}$, $\rm{^3He}$, and $\rm{^3\overline {He}}$ are studied in central collisions of isobars $^{96}_{44}$Ru+$^{96}_{44}$Ru and $^{96}_{40}$Zr+$^{96}_{40}$Zr at $\sqrt{s_{\rm{NN}}}=200$ GeV, using the dynamically constrained phase-space coalescence model and the {\footnotesize PACIAE} model with chiral magnetic effect. The yield, yield ratio, coalescence parameters, and strangeness population factor of (anti-)hypertriton and (anti-)nuclei produced in isobaric $^{96}_{44}$Ru+$^{96}_{44}…
We briefly summarize our recent study on the number of constituent quark (NCQ) scaling of hadron elliptic flows in high multiplicity p-Pb collisions at $\sqrt{s_{NN}}=$ 5.02 TeV. With the inclusion of hadron production via the quark coalescence model at intermediate $p_T$, the viscous hydrodynamics at low $p_T$, and jet fragmentation at high $p_T$, our $Hydro-Coal-Frag$ model provides a nice description of the $p_T$-spectra and differential elliptic flow $v_2(p_T)$ of pions, kaons and protons over the $p_T$ range from 0 to 6 GeV. Our results demonstrate that including the quark coalescence is …
We study the collision energy dependence of (anti-)deuteron and (anti-)triton production in the most central Au+Au collisions at $\sqrt{s_\mathrm{NN}}=$ 7.7, 11.5, 19.6, 27, 39, 62.4 and 200 GeV, using the nucleon coalescence model. The needed phase-space distribution of nucleons at the kinetic freeze-out is generated from a new 3D hybrid dynamical model (\texttt{iEBE-MUSIC}) by using a smooth crossover equation of state (EoS) without a QCD critical point. Our model calculations predict that the coalescence parameters of (anti-)deuteron ($B_2(d)$ and $B_2(\bar{d})$) decrease monotonically as t…
