Production of light nuclei at colliders -- coalescence vs. thermal model
Stanislaw Mrowczynski
备注：
24 pages, 5 figures, final version as in the special volume `Strong Correlations in Dense Matter Physics' of the European Physical Journal ST. arXiv admin note: substantial text overlap with arXiv:2001.11351
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 different in the thermal and coalescence models. The second proposal is to measure a hadron-deuteron correlation function which carries information whether a deuteron is emitted from a fireball together with all other hadrons, as assumed in the thermal model, or a deuteron is formed only after nucleons are emitted, as in the coalescence model. The $p\! -\!^3{\rm He}$ correlation function is of interest in context of both proposals: it is needed to obtain the yield of $^4{\rm Li}$ which decays into $p$ and $^3{\rm He}$, but the correlation function can also tell us about an origin of $^3{\rm He}$.
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 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…
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…
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…
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 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 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…
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）
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…
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…
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…
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 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…
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…
Directed and elliptic flow of light nuclei and hypernuclei in Au+Au collisions at $\sqrt{s_\mathrm{NN}}=3$ GeV: Coalescence vs. Statistical Fragmentation
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.
We review hadron formation from a deconfined quark gluon plasma (QGP) via coalescence or recombination of quarks and gluons. We discuss the abundant experimental evidence for coalescence from the Relativistic Heavy Ion Collider (RHIC) and compare the various coalescence models advocated in the literature. We comment on the underlying assumptions and remaining challenges as well as the merits of the models. We conclude with a discussion of some recent developments in the field.
Quark coalescence models have been applied successfully to reproduce measured hadron production data in relativistic heavy ion collisions at SPS and RHIC energies, which finding strongly supports the formation of deconfined quark matter in these collisions. The investigation of meson and baryon production is an ideal tool to understand dynamical details of hadronization, especially strange hadron numbers and ratios. We display latest results on the production of strange particles in quark coalescence processes in heavy ion collisions at different collider energies.
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 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 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…
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}^{…
We study the production of (hyper-)nuclei and di-baryons in most central heavy Ion collisions at energies of $E_{lab}=1-160 A$ GeV. In particular we are interested in clusters produced from the hot and dense fireball. The formation rate of strange and non-strange clusters is estimated by assuming thermal production from the intermediate phase of the UrQMD-hydro hybrid model and alternatively by the coalescence mechanism from a hadronic cascade model. Both model types are compared in detail. For most energies we find that both approaches agree in their predictions for the yields of the clusters…
Using updated gluon distributions from global fits to data, we investigate the sensitivity of direct photoproduction of heavy quarks and exclusive production of vector mesons to varying strength of gluon modifications. Implications of using these processes for constraining nuclear gluon distributions are discussed.
In very high energy collisions nuclei are practically transparent to each other but produce very hot, nearly baryon-free, matter in the so-called central rapidity region. The energy in the central rapidity region comes from the kinetic energy of the colliding nuclei. We calculate the energy and rapidity loss of the nuclei using the color glass condensate model. This model also predicts the excitation energy of the nuclear fragments. Using a space-time picture of the collision we calculate the baryon and energy densities of the receding baryonic fireballs. For central collisions of gold nuclei …
We show how exclusive vector meson production off light ions can be used to probe the spatial distribution of small-$x$ gluons in the deuteron and $^3$He wave functions. In particular, we demonstrate how short range repulsive nucleon-nucleon interactions affect the predicted coherent $J/Ψ$ production spectra. Fluctuations of the nucleon substructure are shown to have a significant effect on the incoherent cross section above $|t|\gtrsim 0.2\,\mathrm{GeV}^2$. By explicitly performing the JIMWLK evolution, we predict the $x$-dependence of coherent and incoherent cross sections in the EIC energy …
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…
We discuss the production of light nuclei in heavy ion collisions within a multiple freezeout scenario. Thermal parameters extracted from the fits to the observed hadron yields are used to predict the multiplicities of light nuclei. Ratios of strange to non strange nuclei are found to be most sensitive to the details of the chemical freezeout. The well known disagreement between data of $^3_Λ\text{H/}^3\text{He}$ and $\overline{^3_Λ\text{H/}^3\text{He}}$ at $\sqrt{s_{NN}}=200$ GeV and models based on thermal as well as simple coalescence using a single chemical freezeout surface goes away when…
In these proceedings we report recent progress on understanding hadron and jet production in electron-nucleus collisions at the future Electron-Ion Collider [1,2]. These processes will play an essential role in the exploration of the partonic structure of nuclei and the study of parton shower evolution in strongly-interacting matter. We employ the framework of soft-collinear effective theory, generalized to include in-medium interactions, to present the first theoretical results for inclusive hadron and jet cross sections, as well as the jet charge modification in deep inelastic scattering on …
Coalescence has long been used to describe the production of light (anti-)nuclei in heavy ion collisions. The same underlying mechanism may also exist in jets when a proton and a neutron are close enough in phase space to form a deuteron. We model deuteron production in jets by applying an afterburner to protons and neutrons produced in PYTHIA for $p$+$p$ collisions at a center of mass energy $\sqrt{s} =$ 7 TeV. PYTHIA provides a reasonable description of the proton spectra and the shape of the deuteron spectrum predicted by the afterburner is in agreement with the data. We show that the rise …
We show that the recently observed suppression of the yield ratio of deuteron to proton and of helium-3 to proton in p+p collisions compared to those in p+Pb or Pb+Pb collisions by the ALICE Collaboration at the Large Hadron Collider (LHC) can be explained if light nuclei are produced from the coalescence of nucleons at the kinetic freeze-out of these collisions. This suppression is attributed to the non-negligible sizes of deuteron and helium-3 compared to the size of the nucleon emission source in collisions of small systems, which reduces the overlap of their internal wave functions with th…
Using the nucleon coalescence model, which can naturally take into account the correlations in the nucleon density distribution, we study the effects of QCD critical point on light nuclei production in relativistic heavy-ion collisions. We find that the yield ratio $N_tN_p/N_d^2$ of proton ($p$), deuteron ($d$) and triton ($t$) increases monotonically with the nucleon density correlation length, which is expected to increase significantly near the critical point in the QCD phase diagram. Our study thus demonstrates that the yield ratio $N_tN_p/N_d^2$ can be used as a sensitive probe of the QCD…
Based on a covariant coalescence model with a blast-wave-like parametrization for the phase-space configuration of constituent particles at freeze-out, we derive an approximate analytical formula for the yields of clusters produced in relativistic heavy-ion collisions. Compared to previous existing formulae, the present work additionally considers the contributions from the longitudinal dimension in momentum space, the relativistic corrections and the finite size effects of the produced clusters relative to the spatial distribution of constituent particles at freeze-out. The new analytical coa…
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…
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 propose to measure the yields of $^4{\rm He}$ and $^4{\rm Li}$ in relativistic heavy-ion collisions to clarify a mechanism of light nuclei production. Since the masses of $^4{\rm He}$ and $^4{\rm Li}$ are almost equal, the yield of $^4{\rm Li}$ predicted by the thermal model is 5 times bigger than that of $^4{\rm He}$ which reflects the different numbers of internal degrees of freedom of the two nuclides. Their internal structure is, however, very different: the alpha particle is well bound and compact while $^4{\rm Li}$ is weakly bound and loose. Within the coalescence model the ratio of y…
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 nuclei in relativistic heavy-ion collisions is well described by both the thermal model, where light nuclei are in equilibrium with all other hadron species present in a fireball, and by the coalescence model, where light nuclei are formed due to final state interactions after the fireball decays. A method is proposed to falsify one of the models. We suggest to measure a hadron-deuteron correlation function which carries information about the source of the deuterons and allows one to determine whether a deuteron is directly emitted from the fireball or if it is formed a…
We discuss the empirical evidence for a universal Color Glass Condensate and outline prospects for further studies at future colliders. Some ramifications for initial conditions in heavy ion collisions are pointed out.
This work establishes a deep connection between two seemingly distant branches of nuclear physics: nuclear structure and relativistic heavy-ion collisions. At the heart of this connection is the recent discovery made at particle colliders that the elliptic flow of outgoing hadrons in central nucleus-nucleus collisions is strongly impacted by the quadrupole deformation of the colliding nuclear species. I review the physics of the soft sector of relativistic heavy-ion collisions, and I explain that the interpretation of elliptic flow data in central $^{197}$Au+$^{197}$Au, $^{238}$U+$^{238}$U, an…
