On the stability of two-flavor and three-flavor quark matter in quark stars within the framework of NJL model

Following our recently proposed self-consistent mean field approximation approach, we have done some researches on the chiral phase transition of strong interaction matter within the framework of Nambu-Jona-Lasinio (NJL) model. The chiral susceptibility and equation of state (EOS) are computed in this work for both two-flavor and three-flavor quark matter for contrast. The Pauli–Villars scheme, which can preserve gauge invariance, is used in this paper. Moreover, whether the three-flavor quark matter is more stable than the two-flavor quark matter or not in quark stars is discussed in this work. In our model, when the bag constant are the same, the two-flavor quark matter has a higher pressure than the three-flavor quark matter, which is different from what Witten proposed in his pioneering work.

Proper time regularization at finite quark chemical potential

In this paper, we use the two-flavor Nambu–Jona-Lasinio (NJL) model to study the quantum chromodynamics (QCD) chiral phase transition. To deal with the ultraviolet (UV) issue, we adopt the popular proper time regularization (PTR), which is commonly used not only for hadron physics but also for the studies with magnetic fields. This regularization scheme can introduce the infrared (IR) cutoff to include quark confinement. We generalize the PTR to zero temperature and finite chemical potential case use a completely new method, and then study the chiral susceptibility, both in the chiral limit case and with finite current quark mass. The chiral phase transition is second-order in [Formula: see text] and [Formula: see text] and crossover at [Formula: see text] and [Formula: see text]. Three sets of parameters are used to make sure that the results do not depend on the parameter choice.

Susceptibilities and critical exponents within the Nambu–Jona-Lasinio model

In the mean field approximation of (2 + 1)-flavor Nambu–Jona-Lasinio model, we strictly derive several sets of coupled equations for the chiral susceptibility, the quark number susceptibility, etc. at finite temperature and quark chemical potential. The critical exponents of these susceptibilities in the vicinity of the QCD critical end point (CEP) are presented in SU(2) and SU(3) cases, respectively. It is found that these various susceptibilities share almost the same critical behavior near the CEP. The comparisons between the critical exponents for the order parameters and the theoretical predictions are also included.

THE STUDY OF QCD PHASE TRANSITION AT FINITE TEMPERATURE AND CHIRAL CHEMICAL POTENTIAL IN A DYSON–SCHWINGER EQUATION MODEL

In this paper, we use a separable gluon propagator model to study the Quantum Chromodynamics (QCD) phase transition at finite temperature and chiral chemical potential. Using this model, we calculate the quark condensate and the chiral susceptibility at finite temperature and chiral chemical potential both in the chiral limit and at finite current quark mass. Based on these, we obtain the QCD phase diagram in the μ5-T plane.

THE CHIRAL SUSCEPTIBILITY AROUND THE CRITICAL END POINT

This paper is devoted to locate the position of critical end point (CEP) and study its properties. The CEP for different current quark masses are located. It is found that as the current quark mass tends to zero, the position of the CEP tends to the tricrtical point (TCP), while the height of the chiral susceptibility tends to infinity faster and faster, which indicates that the transition from CEP to TCP is continuous. This continuity causes the so-called hidden TCP effect.