2 + 1 Flavors QCD Equation of State in NJL Model with Proper Time Regularization
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I, PARTICLES, FIELDS, GRAVITATION, AND ASTROPHYSICS
2 + 1 Flavors QCD Equation of State in NJL Model with Proper Time Regularization1 Ya-Peng Zhaoa, Cheng-Ming Lia, and Hong-Shi Zonga,b,c,* a Department
of Physics, Nanjing University, Nanjing, 210093 China Center for Particle, Nuclear Physics and Cosmology, Nanjing, 210093 China c State Key Laboratory of Theoretical Physics, Institute of Theoretical Physics, CAS, Beijing, 100190 China * e-mail: [email protected] b Joint
Received November 28, 2017
Abstract—In this paper, we firstly combine the 2 + 1 flavors Nambu-Jona-Lasinio (NJL) model with propertime regularization (PTR) to study the equation of state (EOS) and fix the corresponding parameters in 2 + 1 flavors system. Based on this model, we calculate chiral susceptibility and quark number susceptibility and we find a crossover with chemical potential from 220 to 400 MeV. Then we consider the chemical equilibrium and electric charge neutrality conditions in electroweak reactions, which give some constrains of chemical potentials of different quark flavors. At last, we find that the 2 + 1 flavors system is more stable than 2 flavors system after a comparison and discussion of these two cases. DOI: 10.1134/S106377611807018X
nature are part and parcel of it, and one of the most important of these is chiral symmetry. In particular, the NJL model also exhibits the feature of dynamics chiral symmetry breaking, so it is quite useful for observing how this happens. In 2 flavors (that is, u and d quarks) case, the NJL Lagrangian contains a fourbody interaction, while in three-flavor (that is, u, d, and s quarks) case it contains both four-body and sixbody interaction, which makes the computation simple and convenient. Unfortunately, this model can not be renormalized and doesn’t include confinement. Therefore, we need a procedure for regulating divergent quantities, so, now we introduce the proper-time regularization (PTR) [9–12], i.e., the ultraviolet (UV) momentum cutoff. It can deal with the UV divergence in the model to make the loop integral finite. It is worth noting that the cutoff does not remedy neither the non-renormalizability nor the absence of confinement. In fact the cutoff is only a way to build an effective model with finite predictions in a certain lowenergy domain. And, there are also some other effective models available such as the Dyson-Schwinger equations (DSE) [13–18] and the quark-meson model [19]. As we all know, the equation of state (EOS) of QCD is very important in the calculations about the compact stars [20–25]. Therefore, in this paper, the main goal is to calculate the EOS numerically at zero temperature and finite chemical potential under the condition of chemical equilibrium and electric charge neutrality within the NJL model and PTR regulariza-
1. INTRODUCTION It’s known that Quantum Chromodynamics (QCD) underlies the ground of strong interaction. There are three important characters of QCD, namely, dynamical chiral symmetry breaking (DCSB), asymptotic freedom and quark confinement.
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