Zhu-Fang Cui

Chiral phase transition with a chiral chemical potential in the framework of Dyson-Schwinger equations

Within the framework of Dyson-Schwinger equations , we discuss the chiral phase transition of QCD with a chiral chemical potential μ 5 as an additional scale. We focus especially on the issues related to the widely accepted as well as interesting critical end point (CEP). With the help of a scalar susceptibility, we find that there might be no CEP 5 in the T - μ 5 plane, and the phase transition in the T - μ 5 plane might be totally crossover when μ 50 MeV , which has apparent consistency with the lattice QCD calculation. Our study may also provide some useful hints to some other studies related to μ 5 .

Progress in vacuum susceptibilities and their applications to the chiral phase transition of QCD

The QCD vacuum condensates and various vacuum susceptibilities are all important parameters which characterize the nonperturbative properties of the QCD vacuum. In the QCD sum rules external field formula, various QCD vacuum susceptibilities play important roles in determining the properties of hadrons. In this paper, we review the recent progress in studies of vacuum susceptibilities together with their applications to the chiral phase transition of QCD. The results of the tensor, the vector, the axial–vector, the scalar, and the pseudo-scalar vacuum susceptibilities are shown in detail in the framework of Dyson–Schwinger equations.

Nonlinear susceptibilities under the framework of Dyson-Schwinger equations

Since the baryon-number susceptibilities are correlated with the cumulant of baryon-number fluctuations in experiments, we do calculations of the susceptibilities and compare them with the experimental fluctuation data under the framework of the Dyson-Schwinger equations (DSEs) approach. We compare our results with lattice QCD and experimental data at RHIC. The fitness of the results indicates that under the framework of DSEs, we can deal with the problems of heavy ion collisions properly.

Locate QCD critical end point in a continuum model study

A bstractWith a modified chemical potential dependent effective model for the gluon propagator, we try to locate the critical end point (CEP) of strongly interacting matter in the framework of Dyson-Schwinger equations (DSE). Beyond the chiral limit, we find that Nambu solution and Wigner solution could coexist in some area. Using the CornwallJackiw-Tomboulis (CJT) effective action, we show that these two phases are connected by a first order phase transition. We then locate CEP as the end point of the first order phase transition line. Meanwhile, based on CJT effective action, we give a direct calculation for the chiral susceptibility and thereby study the crossover.

Continuum study of various susceptibilities within thermal QED(3)

In this paper, the relations of four different susceptibilities (i.e., the chiral susceptibility, the fermion number susceptibility, the thermal susceptibility, and the staggered spin susceptibility) are investigated both in and beyond the chiral limit. To this end, we numerically solve the finite-temperature version of the truncated Dyson-Schwinger equations for the fermion and boson propagator. It is found that, in the chiral limit, the four susceptibilities give the same critical temperature and signal a typical second order phase transition. But the situation changes beyond the chiral limit: the critical temperatures from the chiral and the thermal susceptibilities are different, which shows that to define a critical region instead of an exclusive point for crossover might be a more suitable choice. Meanwhile, both the fermion number and the staggered spin susceptibilities have no singular behaviors any more; this may mean that they are no longer available to describe the crossover properties of the system.

Critical end point in the presence of a chiral chemical potential

A class of Polyakov-loop-modified Nambu\char21{}Jona-Lasinio models has been used to support a conjecture that numerical simulations of lattice-regularized QCD defined with a chiral chemical potential can provide information about the existence and location of a critical end point in the QCD phase diagram drawn in the plane spanned by baryon chemical potential and temperature. That conjecture is challenged by conflicts between the model results and analyses of the same problem using simulations of lattice-regularized QCD (lQCD) and well-constrained Dyson-Schwinger equation (DSE) studies. We find the conflict is resolved in favor of the lQCD and DSE predictions when both a physically motivated regularization is employed to suppress the contribution of high-momentum quark modes in the definition of the effective potential connected with the Polyakov-loop-modified Nambu\char21{}Jona-Lasinio models and the four-fermion coupling in those models does not react strongly to changes in the mean field that is assumed to mock-up Polyakov-loop dynamics. With the lQCD and DSE predictions thus confirmed, it seems unlikely that simulations of lQCD with

Critical behaviors near the (tri-)critical end point of QCD within the NJL model

{\ensuremath{\mu}}_{5}g0

Influence of gauge boson mass on the staggered spin susceptibility

can shed any light on a critical end point in the regular QCD phase diagram.

The two-flavor NJL model with two-cutoff proper time regularization

We investigate the dynamical chiral symmetry breaking and its restoration at finite density and temperature within the two-flavor Nambu–Jona–Lasinio model, and mainly focus on the critical behaviors near the critical end point (CEP) and tricritical point (TCP) of quantum chromodynamics. The multi-solution region of the Nambu and Wigner ones is determined in the phase diagram for the massive and massless current quark, respectively. We use the various susceptibilities to locate the CEP/TCP and then extract the critical exponents near them. Our calculations reveal that the various susceptibilities share the same critical behaviors for the physical current quark mass, while they show different features in the chiral limit.

Discussions on the crossover property within the Nambu-Jona-Lasinio model

Based on the study of the linear response of the fermion propagator in the presence of an external scalar field, we calculate the staggered spin susceptibility in the low-energy limit in the framework of the Dyson-Schwinger approach. We analyze the effect of a finite gauge boson mass on the staggered spin susceptibility in both the Nambu phase and the Wigner phase. It is found that the gauge boson mass suppresses the staggered spin susceptibility in the Wigner phase. In addition, we try to give an explanation for why the antiferromagnetic spin correlation increases when the doping is lowered.