QCD phase diagram at finite isospin and baryon chemical potentials with the self-consistent mean field approximation

TL;DR

This paper investigates the QCD phase diagram at finite isospin and baryon chemical potentials using a self-consistent mean field approximation of the NJL model, revealing how phase transition temperatures and critical points depend on model parameters.

Contribution

Introduces a free parameter in the NJL model's mean field approximation to study its effects on the QCD phase structure at finite chemical potentials and temperature.

Findings

Phase transition temperature varies with the parameter lpha and chemical potentials.

Location of the QCD critical end point shifts with lpha.

System transitions from pion superfluidity to normal phase at high eta and low temperature.

Abstract

The self-consistent mean field approximation of two-flavor NJL model with introducing a free parameter $\alpha$ to reflect the competition between "direct" channel and the "exchange" channel, is employed to study QCD phase structure at finite isospin chemical potential $\mu_I$, finite baryon chemical potential $\mu_B$ and finite temperature $T$, especially the location of the QCD critical point. It is found that, for fixed isospin chemical potentials the lower temperature of phase transition is obtained with $\alpha$ increasing in the $T-\mu_I$ plane, and the largest difference of the phase transition temperature with different $\alpha$'s appears at $\mu_I \sim 1.5m_{\pi}$. At $\mu_I=0$ the temperature of the QCD critical end point (CEP) decreases with $\alpha$ increasing, while the critical baryon chemical potential increases. At high isospin chemical potential ($\mu_I=500$ MeV), the temperature of the QCD tricritical point (TCP) increases with $\alpha$ increasing, and in the regions of low temperature the system will transit from pion superfluidity phase to the normal phase as $\mu_B$ increases. At low temperatures, the critical temperature of QCD phase transition with different $\alpha$'s rapidly increases with $\mu_I$ at the beginning, and then increases smoothly around $\mu_I>300$ MeV. In high baryon density region, the increase of the isospin chemical potential will raise the critical baryon chemical potential of phase transition.