Mean-field approximation for the chiral soliton in a chiral phase transition

Using the mean-field approximation, we study the chiral soliton within the linear sigma model in a thermal vacuum. The chiral soliton equations with different boundary conditions are solved at finite temperatures and densities. The solitons are discussed before and after chiral restoration. We find that the system has soliton solutions even after chiral restoration, and that they are very different from those before chiral restoration, which indicates that the quarks are still bound after chiral restoration.

η string formation in QCD chiral phase transition

In the paper we discuss the role of the axial U（1）A symmetry in the chiral phase transition using the U（Nf）R × U（Nf）L linear sigma model with two massless quark flavors. It is expected that above a certain temperature the axial U（1）A symmetry will be restored. A string-like static solution, the η string can be formed and detected in the ultrarelativistic heavy-ion collision process.

Arguing on Entropic and Enthalpic First-Order Phase Transitions in Strongly Interacting Matter

The pattern of isentropes in the vicinity of a first-order phase transition is proposed as a key for a sub-classification. While the confinement-deconfinement transition, conjectured to set in beyond a critical end point in the QCD phase diagram, is often related to an entropic transition and the apparently settled gas-liquid transition in nuclear matter is an enthalphic transition, the conceivable local isentropes w.r.t. “incoming” or “outgoing” serve as another useful guide for discussing possible implications, both in the presumed hydrodynamical expansion stage of heavy-ion collisions and the core-collapse of supernova explosions. Examples, such as the quark-meson model and two-phase models, are shown to distinguish concisely the different transitions.

Phenomenological study of the anisotropic quark matter in the two-flavor Nambu–Jona–Lasinio model

With the two-flavor Nambu–Jona–Lasinio (NJL) model, we carried out a phenomenological study on the chiral phase structure, mesonic properties, and transport properties of momentum-space anisotropic quark matter. To calculate the transport coefficients we utilized the kinetic theory in the relaxation time approximation, where the momentum anisotropy is embedded in the estimation of both the distribution function and relaxation time. It was shown that an increase in the anisotropy parameterξmay result in a catalysis of chiral symmetry breaking. The critical endpoint(CEP) is shifted to lower temperatures and larger quark chemical potentials asξincreases, and the impact of momentum anisotropy on the CEP temperature is almost the same as that on the quark chemical potential of the CEP. The meson masses and the associated decay widths also exhibit a significant ξ dependence. It was observed that the temperature behavior of the scaled shear viscosity η/T~3 and scaled electrical conductivity σ/T exhibited a similar dip structure, with the minima of both η/T~3 and σ/T shifting toward higher temperatures with increasing ξ. Furthermore,we demonstrated that the Seebeck coefficient S decreases when the temperature rises and its sign is positive, indicating that the dominant carriers for converting the temperature gradient to the electric field are up-quarks. The Seebeck coefficient S is significantly enhanced with a largeξfor a temperature below the critical temperature.

Temperature and volume dependence of pion-pion scattering lengths

The s-wave pion-pion scattering lengths a0 and a2 are studied at finite temperature and in finite spatial volume under the framework of the Nambu-Jona-Lasinio model.The behavior beyond the pseudo transition temperature is investigated using proper time regularization.The scattering length a0 exhibits singularity near the Mott temperature,and a2 is a continuous but non-monotonic function of temperature.We present the effect of finite volume on the scattering length and find that a0 can be negative and its singularity disappears at small volumes,which may hint at the existence of a chiral phase transition with decreasing volume.

Phase structures of neutral dense quark matter and applicationto strange stars

In the contact interaction model,the quark propagator has only one solution,namely,the chiral symmetry breaking solution,at vanishing temperature and density in the case of physical quark mass.We generalize the condensate feedback onto the coupling strength from the 2 flavor case to the 2+1 flavor case,and find the Wigner solution appears in some regions,which enables us to tackle chiral phase transition as two-phase coexistences.At finite chemical potential,we analyze the chiral phase transition in the conditions of electric charge neutrality andβequilibrium.The four chemical potentials,μ_(u),μ_(d),μ_(s) and He,are constrained by three conditions,so that one inde-pendent variable remains:we choose the average quark chemical potential as the free variable.All quark masses and number densities suffer discontinuities at the phase transition point.The strange quarks appear after the phase trans-ition since the system needg more energy to produce a d.-quark than an s-quark.Taking the EOS as an input,the TOV equations are solved numerically,and we show that the mass--radius relation is sensitive to the EOS.The max-imum mass of strange quark stars is not susceptible to the parameter Aq we introduced.

Correlations of conserved charges and QCD phase structure

Correlations of conserved charges,i.e.,the baryon number,electric charge,and strangeness,are calculated at finite temperature and chemical potentials up to the fourth order.The calculations are done ina 2+1 flavor low energy effective theory,in which the quantum and thermal fluctuations are encoded through the evolution of flow equations within the functional renormalization group approach.Strangeness neutrality and a fixed ratio of the electric charge to the baryon number density are implemented throughout the computation.We find that higher-order correlations incorporate more sensitive critical dynamics than the quadratic ones.In addition,a non-monotonic dependence of the fourth-order correlations between the baryon number and strangeness,i.e.,-χ_(31)^(BS)/χ_(2)^(S)and χ_(22)^(BS)/χ_(2)^(S),on the collision energy is also observed.

(Pseudo) Scalar mesons in a self-consistent NJL model

In this study, we investigate the mass spectra of π and σ mesons at finite chemical potential using theself-consistent NJL model and the Fierz-transformed interaction Lagrangian. The model introduces an arbitrary parameterα to reflect the weights of the Fierz-transformed interaction channels. We show that, when α exceeds a certainthreshold value, the chiral phase transition transforms from a first-order one to a smooth crossover, which is evidentfrom the behaviors of the chiral condensates and meson masses. Additionally, at a high chemical potential, the smallerthe value of α, the higher the masses of the π and σ mesons. Moreover, the Mott and dissociation chemical potentialsincrease with the increase in α. Thus, the meson mass emerges as a valuable experimental observable for determiningthe value of α and investigating the properties of the chiral phase transition in dense QCD matter.

UA(1)symmetry restoration at high baryon density

We study the relation between chiral and UA(1)symmetries in the quark-meson model.Although quarks and mesons are described in mean field approximation,the topological susceptibility characterizing the UA(1)breaking comprises two components:one controlled by the condensate and the other by the meson fluctuation.The UA(1)restoration is governed by the competition of these components.In a hot medium,the condensates melt.However,the fluctuation is enhanced.Therefore,the UA(1)symmetry cannot be solely restored via the temperature effect.Nevertheless,the baryon density reduces the condensates and fluctuation,and thereby,the UA(1)symmetry can only be restored in a dense or dense and hot medium.The strange condensate plays a weak role in the susceptibility,and the chiral and UA(1)symmetry restorations occur almost at the same critical point.

QCD at finite temperature and density within the fRG approach:an overview

In this paper,we present an overview on recent progress in studies of QCD at finite temperature and densities within the functional renormalization group(fRG)approach.The f RG is a nonperturbative continuum field approach,in which quantum,thermal and density fluctuations are integrated successively with the evolution of the renormalization group(RG)scale.The f RG results for the QCD phase structure and the location of the critical end point(CEP),the QCD equation of state(EoS),the magnetic EoS,baryon number fluctuations confronted with recent experimental measurements,various critical exponents,spectral functions in the critical region,the dynamical critical exponent,etc,are presented.Recent estimates of the location of the CEP from first-principle QCD calculations within f RG and Dyson-Schwinger equations,which pass through lattice benchmark tests at small baryon chemical potentials,converge in a rather small region at baryon chemical potentials of about 600 MeV.A region of inhomogeneous instability indicated by a negative wave function renormalization is found withμ_(B)■420 MeV.It is found that the non-monotonic dependence of the kurtosis of the net-proton number distributions on the beam collision energy observed in experiments could arise from the increasingly sharp crossover in the regime of low collision energy.

Cumulants in the 3-dimensional Ising, O(2) and O(4) spin models

Based on the universal properties of a critical point in different systems and that the QCD phase transitions fall into the same universality classes as the 3-dimensional Ising, O（2） or O（4） spin models, the critical behavior of cumulants and higher cumulant ratios of the order parameter from the three kinds of spin models is studied. We found that all higher cumulant ratios change dramatically the sign near the critical temperature. The qualitative critical behavior of the same order cumulant ratio is consistent in these three models.

Self-consistent mean field approximation and application in three-flavor NJL model

In this study,we apply a self-consistent mean field approximation of the three-flavor Nambu–Jona-Lasinio(NJL)model and compare it with the two-flavor NJL model.The self-consistent mean field approximation introduces a new parameter,α,that cannot be fixed in advance by the mean field approach itself.Due to the lack of experimental data,the parameter,α,is undetermined.Hence,it is regarded as a free parameter and its influence on the chiral phase transition of strong interaction matter is studied based on this self-consistent mean field approximation.αaffects numerous properties of the chiral phase transitions,such as the position of the phase transition point and the order of phase transition.Additionally,increasingαwill decrease the number densities of different quarks and increase the chemical potential at which the number density of the strange quark is non-zero.Finally,we observed thatαaffects the equation of state(EOS)of the quark matter,and the sound velocity can be calculated to determine the stiffness of the EOS,which provides a good basis for studying the neutron star mass-radius relationship.

Longitudinal dynamics from hydrodynamics with an order parameter

We studied coupled dynamics of hydrodynamic fields and order parameter in the presence of nontrivial longitudinal flow using the chiral fluid dynamics model.We found that longitudinal expansion provides an effective relaxation for the order parameter,which equilibrates in an oscillatory fashion.Similar oscillations are also visible in hydrodynamic degrees of freedom through coupled dynamics.The oscillations are reduced when dissipation is present.We also found that the quark density,which initially peaked at the boundary of the boost invariant region,evolves toward forward rapidity with the peak velocity correlated with the velocity of longitudinal expansion.The peak broadens during this evolution.The corresponding chemical potential rises due to simultaneous decrease of density and temperature.We compared the cases with and without dissipation for the order parameter and also the standard hydrodynamics without order parameter.We found that the corresponding effects on temperature and chemical potential can be understood from the conservation laws and different speeds of equilibration of the order parameter in the three cases.