Impact of Vector-Current Interactions on the QCD Phase Diagram

Using a nonlocal version of the Polyakov-loop-extended Nambu-Jona-Lasinio model, we investigate effects of a nonderivative vector-current interaction (relating to the quark-number density) at both real and imaginary chemical potentials. This repulsive vector interaction between quarks has the following impact on the chiral first-order phase transition: at imaginary chemical potential it sharpens the transition at the Roberge-Weiss (RW) end point and moves this critical point toward lower temperatures;at real chemical potential, the critical end point moves on a trajectory towards larger chemical potentials and lower temperatures with increasing vector coupling strength. The conditions are discussed at which the first-order phase transition disappears and turns into a smooth crossover.

QCD phase diagram with the improved Polyakov loop effective potential

We report our recent progress on the QCD phase structure.We explore the properties of quark–gluon matter in the improved Polyakov–Nambu–Jona–Lasinio(PNJL)model by introducing a chemical potential-dependent Polyakov loop potential.This treatment effectively reflects the quantum backreaction of matter sector to glue sector at nonzero chemical potential.Compared with the original PNJL model,a superiority of the improved PNJL model is that it can effectively describe the confinement–deconfinement transition at low temperature and high density.And the QCD phase diagram will be modified to a certain degree if the strength of the quantum backreaction of matter sector to glue sector is strong.One evident variation is that the region of quarkyonic phase will be greatly reduced in the improved PNJL model.This means that the modification to the Polyakov loop potential with the chemical potential dependence is possibly a significant improvement in exploring the full QCD phase structure.

Properties of the phase diagram from the Nambu-Jona-Lasino model with a scalar-vector interaction

We investigated the properties of the phase diagram of high-order susceptibilities,speed of sound,and polytropic index based on an extended Nambu-Jona-Lasinio model with an eight-quark scalar-vector interaction.Non-monotonic behavior was observed in all these quantities around the phase transition boundary,which also revealed the properties of the critical point.Further,this study indicated that the chiral phase transition boundary and critical point could vary depending on the scalarvector coupling constant G_(SV).At finite densities and temperatures,the negative G_(SV)term exhibited attractive interactions,which enhanced the critical point temperature and reduced the chemical potential.The G_(SV)term also affected the properties of the high-order susceptibilities,speed of sound,and polytropic index near the critical point.The non-monotonic(peak or dip)structures of these quantities shifted to a low baryon chemical potential(and high temperature)with a negative G_(SV).G_(SV)also changed the amplitude and range of the nonmonotonic regions.Therefore,the scalar-vector interaction was useful for locating the phase boundary and critical point in QCD phase diagram by comparing the experimental data.The study of the non-monotonic behavior of high-order susceptibilities,speed of sound,and polytropic index is of great interest,and further observations related to high-order susceptibilities,speed of sound,and polytropic index being found and applied to the search for critical points in heavy-ion collisions and the study of compact stars are eagerly awaited.

Color-flavor dependence of the Nambu-Jona-Lasinio model and QCD phase diagram

We study the dynamical chiral symmetry breaking/restoration for various numbers of light quarks flavors N_(f) and colors N_(c) using the Nambu-Jona-Lasinio(NJL) model of quarks in the Schwinger-Dyson equation framework,dressed with a color-flavor dependence of effective coupling.For fixed N_(f)=2 and varying N_(c),we observe that the dynamical chiral symmetry is broken when N_(c) exceeds its critical value N_(c)^(c)≈2.2.For a fixed N_(c)=3 and varying N_(f),we observe that the dynamical chiral symmetry is restored when Nf reaches its critical value N_r^(c)≈8.Strong interplay is observed between N_(c) and N_(f),i.e.,larger values of N_(c) tend to strengthen the dynamical generated quark mass and quark-antiquark condensate,while higher values of N_(f) suppress both parameters.We further sketch the quantum chromodynamics(QCD) phase diagram at a finite temperature T and quark chemical potential μ for various N_(c) and N_(f).At finite T and μ,we observe that the critical number of colors N_(c)^(c) is enhanced,whereas the critical number of flavors N_(f)^(c) is suppressed as T and μ increase.Consequently,the critical temperature T_(c),μ_(c),and co-ordinates of the critical endpoint(T_(c)^(E),μ_(c)^(E)) in the QCD phase diagram are enhanced as N_(c) increases and suppressed when N_(f) increases.Our findings agree with the lattice QCD and Schwinger-Dyson equations predictions.

相对论重离子碰撞中QCD相图的实验研究

量子色动力学(Quantum Chromodynamics,QCD)相图结构和相变临界点是高能物理理论和实验的研究热点。相对论重离子碰撞是探索QCD相图结构、寻找QCD相变临界点的有力工具。美国布鲁克海文国家实验室的相对论重离子对撞机(Relativistic Heavy Ion Collider,RHIC)是目前世界上进行高能重离子碰撞的大型实验装置之一,其中的STAR(Solenoidal Tracker at RHIC)实验致力于高温高密条件下夸克胶子等离子体(Quark Gluon Plasma,QGP)性质以及QCD相结构的实验研究。本文着重介绍近年来RHIC-STAR能量扫描实验中运用守恒荷高阶矩和轻核产生寻找QCD相变临界点的研究进展,最后将对高重子密度区QCD相结构的未来研究做出展望。

QCD临界点附近的动力学临界涨落

探寻量子色动力学(Quantum Chromodynamics,QCD)相图的临界点是相对论重离子碰撞实验低能量扫描(Beam Energy Scan program in Relativistic Heavy-Ion Collisions,RHIC-BES)项目的重要实验目标。初步的实验探测发现了净质子数涨落随着对撞能量的非单调行为,定性上符合基于静态模型的理论预言,这暗示着QCD临界点的存在。由于相对论重离子碰撞是一个高速膨胀的体系,动力学效应能显著地改变QCD临界点附近的临界涨落。为最终确定QCD临界点的存在以及研究QCD在有限温有限密区域的相结构,人们发展了一系列QCD临界点附近的动力学模型。本文回顾了近年来关于寻找QCD临界点在实验测量和理论模型的进展,着重强调在临界点及一级相变区域动力学模型的发展和挑战。

BEST合作组QCD相图研究进展

能量扫描理论合作组(Beam Energy Scan Theory Collaboration,BEST)的目标是建立一个可以描述美国相对论重离子对撞机(Relativistic Heavy-Ion Collider,RHIC)上第二期能量扫描实验的动力学框架。该实验有可能找到强相互作用相图上的临界点。本文总结自2016年起,BEST合作组取得重要进展,并对未来探索中高密度区相图做了展望。

基于有效场论的QCD相图研究

量子色动力学(Quantum Chromodynamics,QCD)相图是高能核物理领域研究的前沿热点。本文基于有效场论的方法,包括Nambu-Jona-Lasinio模型和Dyson-Schwinger方程等,介绍了近期QCD相图研究的多方面进展,包括利用高阶磁化率寻找相变信号,手征不平衡、有限体积和旋转等对相图的影响,以及QCD物态方程在致密星体中的应用。研究发现,重子数高阶涨落的理论结果与实验测量的质子数高阶矩可以较好地符合;手征不平衡、有限体积和旋转对手征凝聚和相图结构都有一定的影响;从有效场论的QCD物态方程出发,可以给出符合脉冲星观测的结果。

QCD临界终点与重子数扰动

相对论性重离子对撞的目的之一是寻找量子色动力学(Quantum Chromodynamics,QCD)临界终点(Critical End Point,CEP),实验中测到的净质子数扰动呈现出非单调的行为,这暗示了CEP的存在。本文使用了3味PNJL(Polyakov-loop Nambu-Jona-Lasinio)模型,沿着从实验数据中拟合的化学冻结线,计算了重子数扰动累积量之比C4/C2随对撞能量的变化。结果发现,基于平衡态假设,在对撞能量7.7~200 GeV范围内,随着对撞能量的降低,C4/C2先缓慢下降后上升,这与实验数据一致。这也暗示平衡态假设可以用于探索重离子对撞后系统的演化行为,揭示了相变线跟化学冻结线的关系对观测量的影响非常重要。

极强磁场与QCD相图

本文总结了极强磁场下量子色动力学(Quantum Chromodynamics,QCD)相变的研究现状和许多新进展,包括格点QCD和有效手征模型的计算结果。涉及的QCD相如下:手征对称性破缺、手征对称性恢复、非均匀手征相、π0凝聚、π超流、ρ凝聚以及色超导。除了强磁场B外,这些相的实现和相互转化还要同时考虑其他效应的共同作用,比如温度T、强电场E、各种化学势μ或转动角速度Ω等。与之对应,介绍一些由磁场和这些物理参量共同张成的相图:T-B相图、E-B相图、μB-B相图、μI-B相图以及Ω-B相图,并阐述相变背后的物理机制。

Thermodynamic properties and phase diagram of quark matter within non-extensive Polyakov chiral SU(3)quark mean field model

In the present study,we applied Tsallis non-extensive statistics to investigate the thermodynamic properties and phase diagram of quark matter in the Polyakov chiral SU(3)quark mean field model.Within this model,the properties of the quark matter were modified through the scalar fieldsσ,ζ,δ,χ,vector fieldsω,ρ,ϕ,and Polyakov fieldsΦandΦ¯at finite temperature and chemical potential.Non-extensive effects were introduced through a dimensionless parameter q,and the results were compared to those of the extensive case(q→1).In the non-extensive case,the exponential in the Fermi-Dirac(FD)function was modified to a q-exponential form.The influence of the q parameter on the thermodynamic properties,pressure,energy,and entropy density,as well as trace anomaly,was investigated.The speed of sound and specific heat with non-extensive effects were also studied.Furthermore,the effect of non-extensivity on the deconfinement phase transition as well as the chiral phase transition of u,d,and s quarks was explored.We found that the critical end point(CEP),which defines the point in the(T−μ)phase diagram where the order of the phase transition changes,shifts to a lower value of temperature,TCEP,and a higher value of chemical potential,μCEP,as the non-extensivity is increased,that is,q>1.

Nonextensive effects on QCD chiral phase diagram and baryon-number fluctuations within Polyakov-Nambu-Jona-Lasinio model

In this paper,a version of the Polyakov-Nambu-Jona-Lasinio(PNJL)model based on nonextensive statistical mechanics is presented.This new statistics summarizes all possible factors that violate the assumptions of the Boltzmann-Gibbs(BG)statistics to a dimensionless nonextensivity parameter q.Thus,when q tends to 1,it returns to the BG case.Within the nonextensive PNJL model,we found that as q increases,the location of the critical end point(CEP)exhibits non-monotonic behavior.That is,for q<1.15,CEP moves in the direction of lower temperature and larger quark chemical potential.However,for q>1.15,CEP turns to move in the direction of lower temperature and lower quark chemical potential.In addition,we studied the moments of the net-baryon number distribution,that is,variance(σ^(2)),skewness(S),and kurtosis(k).Our results are generally consistent with the latest experimental data reported,especially for√SNN>19.6 GeV,when q is set to 1.07.

Matter-Antimatter Coexistence Method for Finite Density QCD toward a Solution of the Sign Problem

Toward the lattice QCD calculation at finite density, we propose “matter-antimatter coexistence method”, where matter and anti-matter systems are prepared on two parallel R4-sheets in five-dimensional Euclidean space-time. We put a matter system M with a chemical potential &mu;&isin;C on a R4-sheet, and also put an anti-matter system withon the other R4-sheet shifted in the fifth direction. Between the gauge variables? in M and in, we introduce a correlation termwith a real parameter &lambda;. In one limit of , a strong constraint is realized, and therefore the total fermionic determinant becomes real and non-negative, due to the cancellation of the phase factors in M and , although this system resembles QCD with an isospin chemical potential. In another limit of , this system goes to two separated ordinary QCD systems with the chemical potential of &mu;and . For a given finite-volume lattice, if one takes an enough large value of &lambda;, is realized and phase cancellation approximately occurs between two fermionic determinants in M and, which suppresses the sign problem and is expected to make the lattice calculation possible. For the obtained gauge configurations of the coexistence system, matter-side quantities are evaluated through their measurement only for the matter part M. The physical quantities in finite density QCD are expected to be estimated by the calculations with gradually decreasing &lambda;and the extrapolation to &lambda;=0. We also consider more sophisticated improvement of this method using an irrelevant-type correlation.

Anisotropic flow in high baryon density region

Collective flow is a powerful tool used to analyze the properties of a medium created during high-energy nuclear collisions.Here,we report a systematic study of the first two Fourier coefficients v_(1)and v_(2)of the proton andπ^(+)from Au+Au collisions in the energy range√sNN=2.11-4.9 GeV within the framework of a hadronic transport model(UrQMD).Recent results from the STAR experiment were used to test the model calculations.A meanfield mode with strong repulsive interaction is needed to reproduce the 10-40%data at 3 GeV.This implies that hadronic interactions play an important role in the collective flow development in the high baryon density region.The mean values of the freeze-out time for protons andπ^(+)are shifted earlier owing to the additional repulsive interactions.We predict the energy dependence of the mean values of the transverse momentum<pT>,v_(1),and v_(2)for both protons andπ^(+)from the Au+Au collisions.

Nonextensive effects on QCD chiral phase transition with a chiral chemical potential

In this study,we investigate the QCD chiral phase diagram in the presence of a chiral chemical potential μ based on nonextensive statistical mechanics.A feature of this new statistic is a dimensionless nonextensivity parameter q,which summarizes all possible effects violating the assumptions of Boltzmann-Gibbs(BG)statistics(when q→1,it returns to the BG case).Within the nonextensive Polyakov-Nambu-Jona-Lasinio model,we find that as μ increases,the critical end point(CEP)in the T-μ plane continues to CEP_(5)in the T-μ plane,and nonextensive effects have a significant impact on the evolution from the CEP to CEP_(5).Generally,with an increase in q,both the CEP and CEP_(5)move in the direction of a lower temperature T and larger chemical potentialμ(μ_(5)).In addition,we find that chiral charge density ngenerally increases with T,μ,μ_(5),and q.Our study may provide useful hints about lattice QCD and relativistic heavy-ion collision experiments.

Critical Line Back-Bending Induced either by Finite N_(c)Corrections or by a Repulsive Vector Channel

We analyze the two flavor version of the Nambu-Jona-Lasinio model with a repulsive vector coupling (GV), at finite temperature and quark chemical potential, in the strong scalar coupling (Gs) regime. Considering GV = 0, we review how finite Nc effects are introduced by means of the Optimized Perturbation Theory (OPT) which adds a term to the thermodynamical potential. This 1/ Nc suppressed term is similar to the contribution obtained at the large-Nc limit when GV ≠ 0. Then, scanning over the quark current mass values, we compare these two different model approximations showing that both predict the appearance of two critical points when chiral symmetry is weakly broken. By mapping the first order transition region in the chemical potential-current mass plane, we show that, for low chemical potential values, the first order region shrinks as μ increases but the behavior gets reversed at higher values leading to the back-bending of the critical line. This result, which could help to conciliate some lattice results with model predictions, shows the important role played by finite Nc corrections which are neglected in the majority of the works devoted to the determination of the QCD phase diagram. Recently the OPT, with GV = 0, and the large-Nc approximation, with GV ≠ 0, were compared at zero temperature and finite density for one quark flavor only. The present work extends this comparison to finite temperatures, and two quark flavors, supporting the result that the OPT finite

Explore the QCD phase transition phenomena from a multiphase transport model

We study the phase structure of QCD matter in the framework of a multiphase transport model by implementing a strong local parton density fluctuation scenario. Our calculations on the beam energy dependence of net-proton high moment show that local parton density fluctuation only has a small effect. But it becomes important when all baryons are included. We then study the effect on elliptic flow and find that an enhanced local parton density fluctuation leads to a significant effect on protons but a small effect on pions. Our study provides a reference of transport dynamics on QCD phase transition phenomena and will be relevant for the upcoming phase II of the beam energy scan program at RHIC.

基于pNJL模型的三维QCD相图

基于三味Polyakov-looped Nambu-Jona-Lasinio(pNJL)模型,通过研究手征凝聚、pion凝聚和Polyakov圈之间的相互作用,研究了温度、重子化学势和同位旋化学势依赖的三维QCD相图结构。虽然pNJL模型得到的正常夸克物质相、pion超流相和Sarma相的结构以及相边界与NJL模型定性上相似,但Polyakov圈的引入大大扩展了pion超流相和Sarma相的存在区域,并导致临界点出现在较高的温度。由于有效地引入了胶子动力学的贡献,与NJL模型相比,该研究有望对三维QCD相图给出更可靠的预测。

Nucleon Mass Splitting at Finite Isospin Chemical Potential

We investigate nucleon mass splitting at finite isospin chemical potential in the frame of the two-flavour Nambu-Jona-Lasinio model. It is analytically proven that in the phase with explicit isospin symmetry breaking, the proton mass decreases and the neutron mass increases linearly in the isospin chemical potential.

Restriction on the form of the quark anomalous magnetic moment from lattice QCD results

The quark anomalous magnetic moment(AMM)is dynamically generated through spontaneous chiral symmetry breaking.It has been revealed that,even though its exact form is still unknown,the quark AMM is essential to exploring quark matter properties and QCD phase structure under external magnetic fields.In this study,we take three different forms of the quark AMM and investigate its influence on the chiral phase transition under a magnetic field.In general,a negative(positive)quark AMM acts as a magnetic-catalyzer(magnetic-inhibitor)for chiral symmetry breaking.It is found that a constant quark AMM drives an unexpected 1st order chiral phase transition,a quark AMM proportional to the chiral condensate flips the sign on the chiral condensate,and a quark AMM proportional to the square of the chiral condensate suppresses the magnetic enhancement in the chiral condensate at finite temperatures while retaining the chiral crossover phase transition.We also evaluate the intrinsic temperature dependence of the effective AMM form by fitting the effective model result of the chiral condensate to lattice QCD data,which may have a nontrivial correlation with the chiral phase transition.