We develop a new formulation of the quark coalescence model by including the quark number conservation in order to describe the hadronization of the bulk of the quark-gluon plasma. The scalings between hadron and quark phase space distributions are shown to depend on the transverse momentum. For hard quarks, our general scalings reproduce the usual quadratic scaling relation for mesons and the cubic scaling relation for baryons. For softer quarks, however, the inclusion of the quark number conservation leads to a linear scaling for the hadron species that dominates the quark number of each flavor, while the scalings of non-dominant hadrons depend on the coalescence dynamics. For charm mesons, we find that the distribution of soft $D$ mesons does not depend on the light quark distribution but the distribution of soft $J/ψ$ mesons is inversely correlated to the light quark distribution.
Heavy quarks are initially produced in nuclear collisions and the number is conserved during the evolution of the system. We establish a sequential coalescence model with charm conservation and apply it to charmed hadron production at RHIC and LHC energies. The charm conservation enhances the earlier formed hadrons and reduces the later formed ones, which leads to a $D_s/D^0$ enhancement and a $Λ_c/D^0$ suppression. The mass dependence of the sequential hadron formation provides us a new tool for studying the quark-gluon plasma hadronization in high energy nuclear collisions.
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…
Hydrodynamics and jet quenching are responsible for the elliptic flow $v_2$ and suppression of large transverse momentum ($p_T$) hadrons, respectively, two of the most important phenomena leading to the discovery of a strongly coupled quark-gluon plasma (QGP) in high-energy heavy-ion collisions. A consistent description of the hadron suppression factor $R_{AA}$ and $v_2$, especially at intermediate $p_T$, however, remains a challenge. We solve this long-standing $R_{AA}\otimes v_2$ puzzle by including quark coalescence for hadronization and final state hadron cascade in the coupled linear Bolt…
Different scenarios for the creation of constituent mass in the hadron formation process are discussed. Effects of these may be observable in hadron momentum spectra.
Elliptic flow of charm hadrons is investigated based on the quark coalescence model. Due to the large difference between the charm quark and light quark masses, hadrons containing both light and charm quarks show a qualitatively different $v_2(p_\perp)$ from hadrons containing only light quarks. Simple relations are proposed to infer quark elliptic flow from those of hadrons. The effects of the finite momentum spread of hadron wavefunctions are also studied, and are found to be small for charm hadrons.
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.
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.
We review the quark coalescence model for hadronization in relativistic heavy ion collisions and show how it can explain the observed large baryon to meson ratio at intermediate transverse momentum and scaling of the elliptic flows of identified hadrons. We also show its predictions on higher-order anisotropic flows and discuss how quark coalescence applied to open- and hidden-charm mesons can give insight to charm quark interactions in the quark-gluon plasma and $J/Ψ$ production in heavy ion collisions.
The coalescence model assumes instant formation of a bound state from unbound particles based on the overlapping of two states in spatial and momentum spaces and quantum numbers. Therefore, applied to the hadronization of partons, it provides a snapshot of a Quark-Gluon Plasma (QGP) just before hadronization. We use the coalescence model for the formation of the ground state of open heavy flavor and the statistical model for heavier states. Assuming that all heavy flavors in thermal equilibrium hadronize through the coalescence, we find that the QGP just before hadronization is not composed of…
The production of particles with double, triple and hidden charm in heavy ion collisions is studied in the framework of the statistical coalescence model. According to the postulates of the model, the charm quark-antiquark pairs are created at the initial stage of a heavy ion reaction in hard parton collisions. The amount of charm is assumed to be unchanged at later stages. The charm (anti)quarks are distributed among different hadron species at hadronization according to the laws of statistical physics. Several approaches to the statistical treatment of charm hadronization are considered. The…
Recent experimental data support the presence of quark coalescence in heavy ion collisions at RHIC energies. Hadronization of quark matter and hadron formation in heavy ion collisions can be described by the coalescence process, and measured data are reproduced successfully. On the other hand, the theoretical coalescence calculations are based on a non-relativistic description. Here we investigate the robustness of the coalescence description, using different wave-function overlap during hadron formation.
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.
The problem of hadronic cluster production in quark-hadron phase transition in heavy-ion collisions is studied by cellular automata. Previous result on the scaling behavior is extended to include variation in the drift speed. It is also shown that coalescence is more important than growth in generating scaling. A new set of rules is adopted to free the clusters from being rigid. It is found that the scaling exponent is independent of not only the shapes of the clusters, but also the probability of breakup of the clusters. The universality of the scaling behavior is now extended to a wide range…
We propose an improved quark coalescence model for spin alignment of vector mesons and polarization of baryons by spin density matrix with phase space dependence. The spin density matrix is defined through Wigner functions. Within the model we propose an understanding of spin alignments of vector mesons $ϕ$ and $K^{*0}$ (including $\bar{K}^{*0}$) in the static limit: a large positive deviation of $ρ_{00}$ for $ϕ$ mesons from 1/3 may come from the electric part of the vector $ϕ$ field, while a negative deviation of $ρ_{00}$ for $K^{*0}$ may come from the electric part of vorticity tensor fields…
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 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…
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…
We show that hadronization via quark coalescence enhances hadron elliptic flow at large pT relative to that of partons at the same transverse momentum. Therefore, compared to earlier results based on covariant parton transport theory, more moderate initial parton densities dN/dη(b=0) ~ 1500-3000 can explain the differential elliptic flow v_2(pT) data for Au+Au reactions at s^1/2=130 and 200 AGeV from RHIC. In addition, v2(pT) could saturate at about 50% higher values for baryons than for mesons. If strange quarks have weaker flow than light quarks, hadron v_2 at high pT decreases with relative…
The large and saturating differential elliptic flow v2(pT) observed in Au+Au reactions at RHIC so far could only be explained assuming an order of magnitude denser initial parton system than estimated from perturbative QCD. Hadronization via parton coalescence can resolve this ``opacity puzzle'' because it enhances hadron elliptic flow at large pT relative to that of partons at the same transverse momentum. An experimentally testable consequence of the coalescence scenario is that v2(pT) saturates at about 50% higher values for baryons than for mesons. In addition, if strange quarks have weake…
Production of $c\bar c$ pairs in elementary hadron-hadron collisions is introduced in a simulation of relativistic heavy ion collisions. Coalescence of charmed quarks and antiquarks into various charmonium states is performed and the results are compared to PHENIX J$/ψ$ Au+Au data. The $χ$ and $ψ$' bound states must be included as well as the ground state J$/ψ$, given the appreciable feeding from the excited states down to the J$/ψ$ via gamma decays. Charmonium coalescence is found to take place at relatively late times: generally after $c$($\bar c$)-medium interactions have ceased. Direct pro…
In a coalescence plus independent fragmentation approach we calculate the $p_T$ spectra of the main hadrons: $π, K, p, \bar p, Λ, ϕ$ in a wide range of transverse momentum from low $p_T$ up to about 10 GeV. The approach in its main features was developed several years ago at RHIC energy. Augmenting the model with the inclusion of some more main resonance decays, we show that the approach correctly predicts the evolution of the $p_T$ spectra from RHIC to LHC energy and in particular the baryon-to-meson ratios $p/π,\bar p/π,Λ/K$ that reach a value of the order of unit at $p_T \sim 3\, \rm GeV$. …
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…
Heavy flavor supplies a chance to constrain and improve the hadronization mechanism. We have established a sequential coalescence model with charm conservation and applied it to the charmed hadron production in heavy ion collisions. The charm conservation enhances the earlier hadron production and suppresses the later production. This relative enhancement (suppression) changes significantly the ratios between charmed hadrons in heavy ion collisions.
The Hadron Resonance Gas Model with two chemical freeze-outs, connected by conservation laws is considered. We are arguing that the chemical freeze-out of strange hadrons should occur earlier than the chemical freeze-out of non-strange hadrons. The hadron multiplicities measured in the heavy ion collisions for the center of mass energy range 2.7 - 200 GeV are described well by such a model. Based on a success of such an approach, a radical way to improve the Hadron Resonance Gas Model performance is suggested. Thus, we suggest to identify the hadronic reactions that freeze-out noticeably earli…
Assuming the Statistical Hadronization Model and charm flavour conservation, one can quantify the deviation of charm and anti-charm quarks from chemical equilibrium both in the hadronic phase and in the quark-gluon plasma. By linking the hadronic fireball volume and the corresponding plasma source volume via entropy conservation as proposed by Grandchamp et al., a direct comparison between the $J/ψ$ yields in both pictures can be used to obtain limits for the charm quark mass in the medium.
We review the application and successes of a phase-space coalescence plus fragmentation model that has been applied for hadronization at RHIC. The physical concept is discussed together with the practical implementation. The robustness of main predictions is reviewed together with several open issues like relevance of three dimensional calculation, finite width of the wave functions, effects of quark masses, energy-entropy conservation, space-momentum correlation. Eventually the relevance of coalescence also for the study of the microscopic interaction of heavy quarks is highlighted.
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.
The production rate of negative parity baryons was found to be much weaker than that of positive states in RHIC experiments. In the present paper we show that this suppression is a simple consequence of the coalescence dynamics of hadronization.
The string melting version of a multi-phase transport model is often applied to high-energy heavy-ion collisions since the dense matter thus formed is expected to be in parton degrees of freedom. In this work we improve its quark coalescence component, which describes the hadronization of the partonic matter to a hadronic matter. We removed the previous constraint that forced the numbers of mesons, baryons, and antibaryons in an event to be separately conserved through the quark coalescence process. A quark now could form either a meson or a baryon depending on the distance to its coalescence …
A study of elliptic flow of open charm mesons, $D^0$ and $D_S ^\pm$ using quark coalescence as a mechanism of hadronization of heavy quarks implemented in conjunction with A Multi Phase Transport (AMPT) model has been presented. We have studied the transverse momentum dependence of the elliptic flow parameter at mid-rapidity ($|y|$ $<$ 1.0) for Au+Au collisions at $\sqrt{s_{NN}} = 200$ GeV (RHIC) and Pb+Pb collisions at $\sqrt{s_{NN}} = 2.76$ TeV (LHC) for different values of partonic interaction cross-section and QCD coupling constant. We have compared our calculations with the experimentally…
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…
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…
We employ the Boltzmann equation for describing hadron production from a quark-gluon plasma (QGP) in ultrarelativistic heavy-ion collisions. We propose resonance formation in quark-antiquark scattering as the dominant meson-production channel, which, in particular, ensures that energy is conserved in the recombination process. This, in turn, facilitates a more controlled extension of hadronization to low transverse momenta ($p_T$), and to address the experimentally observed transition from a hydrodynamic regime to constituent quark-number scaling (CQNS). Based on input distributions for strang…
We show that either mass ordering or quark number scaling of anisotropic flow can result from quark coalescence, depending on the nature of phase space correlations at hadronization. Quark number scaling signals nonequilibrium dynamics because it can only appear when hydrodynamic correlations break down. However, the scaling does not hold for all nonthermal distributions, and is compatible with covariant transport theory only if remarkable cancellations occur at RHIC.
We construct a theoretical framework to describe the evolution of heavy flavors produced in relativistic heavy-ion collisions. The in-medium energy loss of heavy quarks is described using our modified Langevin equation that incorporates both quasi-elastic scatterings and the medium-induced gluon radiation. The space-time profiles of the fireball is described by a (2+1)-dimensional hydrodynamics simulation. A hybrid model of fragmentation and coalescence is utilized for heavy quark hadronization, after which the produced heavy mesons together with the soft hadrons produced from the bulk QGP are…
We study the production of multi-charmed hadrons by recombination in heavy ion collisions by focusing on the production of $Ξ_{cc}$, $Ξ_{cc}^*$, $Ω_{scc}$, $Ω_{scc}^*$, $Ω_{ccc}$ baryons and X(3872) mesons. Starting from the estimation of yields for those hadrons at chemical freeze-out in both the statistical and coalescence model, we evaluate their transverse momentum distributions at mid-rapidity in the coalescence model. We show that yields of multi-charmed hadrons in heavy ion collisions at RHIC and LHC are large enough, and thereby not only multi-charmed hadrons observed so far, e.g., the…
We explore the effect of hadronization by partonic coalescence on a "conical" signal at the partonic level. We show that, by transferring partons from a lower to a higher $p_T$, coalescence makes the conical signal stronger and hence less susceptible to thermal smearing, provided the signal is integrated over a large momentum bin and effects such as non-collinearity and a finite Wigner function width are taken into account. We explore the role of this effect in baryon/meson scaling and calculate the effect of resonances decays on such a conical signal.
Recent data for the ratio $R(Q)= QF_{2}(Q^{2})/F_{1}(Q^{2})$ shocked the community by disobeying expectations held for 50 years. We examine the status of perturbative QCD predictions for helicity-flip form factors. Contrary to common belief, we find there is no rule of hadron helicity conservation for form factors. Instead the analysis yields an inequality that the leading power of helicity-flip processes may equal or exceed the power of helicity conserving processes. Numerical calculations support the rule, and extend the result to the regime of laboratory momentum transfer $Q^{2}$. Quark orb…
Hagedorn states are characterized by being very massive hadron-like resonances and by not being limited to quantum numbers of known hadrons. To generate such a zoo of different Hagedorn states, a covariantly formulated bootstrap equation is solved by ensuring energy conservation and conservation of baryon number $B$, strangeness $S$ and electric charge $Q$. The numerical solution of this equation provides Hagedorn spectra, which enable to obtain the decay width for Hagedorn states needed in cascading decay simulations. A single (heavy) Hagedorn state cascades by various two-body decay channels…
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 statistical production of antibaryons is considered within the canonical ensemble formulation. We demonstrate that the antibaryon suppression in small systems due to the exact baryon number conservation is rather different in the baryon-free (B=0) and baryon-rich (B>1) systems. At constant values of temperature and baryon density in the baryon-rich systems the density of the produced antibaryons is only weakly dependent on the size of the system. For realistic hadronization conditions this dependence appears to be close to B/(B+1) which is in agreement with the preliminary data of the NA49…
The problem of cluster formation and growth in first-order quark-hadron phase transition in heavy-ion collisions is considered. Behaving as Brownian particles, the clusters carry out random walks and can encounter one another, leading to coalescence and breakup. A simulation of the process in cellular automaton suggests the possibility of a scaling distribution in the cluster sizes. The experimental determination of the cluster-size distribution is urged as a means to find a clear signature of phase transition.
We revisit the problem of particlization of a QCD fluid into hadrons and resonances at the end of the fluid dynamical stage in relativistic heavy-ion collisions in a context of fluctuation measurements. The existing methods sample an ideal hadron resonance gas, therefore, they do not capture the non-Poissonian nature of the grand-canonical fluctuations, expected due to QCD dynamics such as the chiral transition or QCD critical point. We address the issue by partitioning the particlization hypersurface into locally grand-canonical fireballs populating the space-time rapidity axis that are const…
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 …
Higher moments of multiplicity fluctuations of hadrons produced in central nucleus-nucleus collisions are studied within the hadron-resonance gas model in the canonical ensemble. Exact conservation of three charges, baryon number, electric charge, and strangeness, is enforced in the large volume limit. Moments up to the forth order of various particles are calculated at SPS, RHIC and LHC energies. The asymptotic fluctuations within a simplified model with only one conserved charge in the canonical ensemble are discussed where simple analytical expressions for moments of multiplicity distributi…
Flow plus coalescence explain hadron nuclear modification and high-$p_T$ anisotropy
CERN（欧洲核子研究中心）；Utrecht University（乌得勒支大学）；NIKHEF（荷兰国家核物理与粒子物理研究所）；University of the Witwatersrand（威特沃特斯兰德大学）；National Institute for Theoretical and Computational Sciences（理论与计算科学国家研究所）
Here we thoroughly discuss some weak points of the thermal model which is traditionally used to describe the hadron multiplicities measured in the central nucleus-nucleus collisions. In particularly, the role of conservation laws, the values of hard-core radii along with the effects of the Lorentz contraction of hadron eigen volumes and the hadronic surface tension are systematically studied. It is shown that for the adequate description of hadron multiplicities the conservation laws should be modified, whereas for the description of hadron yield ratios the conservation laws are not necessary …
We develop for charmed hadron production in relativistic heavy-ion collisions a comprehensive coalescence model that includes an extensive set of $s$ and $p$-wave hadronic states as well as the strict energy-momentum conservation, which ensures the boost invariance of the coalescence probability and the thermal limit of the produced hadron spectrum. By combining our hadronization scheme with an advanced Langevin-hydrodynamics model that incorporates both elastic and inelastic energy loss of heavy quarks inside the dynamical quark-gluon plasma, we obtain a successful description of the $p_\math…
Based on the quark coalescence model for the parton-to-hadron phase transition in ultra-relativistic heavy ion collisions, we relate the elliptic flow ($v_2$) of high $\pt$ hadrons to that of high $\pt$ quarks. For high $\pt$ hadrons produced from an isospin symmetric and quark-antiquark symmetric partonic matter, magnitudes of their elliptic flows follow a flavor ordering as $(v_{2,π}=v_{2,N}) > (v_{2,Λ}=v_{2,Σ}) > v_{2,K} > v_{2,Ξ} > (v_{2,ϕ}=v_{2,Ω})$ if strange quarks have a smaller elliptic flow than light quarks. The elliptic flows of high $\pt$ hadrons further follow a simple quark coun…
We show that particle species dependence of enhanced hadron production at intermediate transverse momentum (p_{T}) for d+Au collisions at RHIC can be understood in terms of the hadronic rescatterings in the final state. A multiphase transport model (AMPT) with two different hadronization mechanisms: string fragmentation or parton coalescence, is used in our study. When the hadrons are formed from string fragmentation, the subsequent hadronic rescatterings will result in particle mass dependence of nuclear modification factor R_{CP}, which is consistent with the present experimental data. On th…
The study of fluctuations of particle multiplicities in relativistic heavy-ion reactions has drawn much attention in recent years, because they have been proposed as a probe for underlying dynamics and possible formation of quark-gluon plasma. Thus, it is of uttermost importance to describe the baseline of statistical fluctuations in the hadron gas phase in a correct way. We have performed a comprehensive study of multiplicity distributions in the full ideal hadron-resonance gas in different ensembles, namely grand-canonical, canonical and microcanonical, using two different methods: asymptoti…
Studies of beauty hadron and non-prompt charm hadron production in pp collisions at $\sqrt{s}$=13 TeV within a transport model approach
School of Mathematics and Physics, China University of Geosciences (Wuhan)（中国地质大学（武汉）数学与统计学院）；Key Laboratory of Quark and Lepton Physics (MOE) and Institute of Particle Physics, Central China Normal University（华中师范大学夸克与轻子物理教育部重点实验室及粒子物理研究所）；Shanghai Research Center for Theoretical Nuclear Physics, NSFC and Fudan University（复旦大学理论核物理上海研究中心）
