Current quark mass and nonzero-ness of chiral condensates in thermal Nambu-Jona-Lasinio model

TL;DR

This paper reexamines how a nonzero current quark mass influences chiral condensates in a thermal NJL model, showing that complete restoration of chiral symmetry is physically unrealistic, affecting phase transition characteristics.

Contribution

It provides a systematic analysis demonstrating that nonzero quark mass prevents full chiral symmetry restoration in the NJL model at finite temperature and chemical potential.

Findings

Nonzero quark mass leads to persistent chiral condensates.

Complete chiral symmetry restoration requires unrealistic conditions.

Results influence understanding of phase transitions and the QCD phase diagram.

Abstract

The effect that the current quark mass $M_0$ may result in nonzero-ness of chiral condensates is systematically reexamined and analyzed in a two-flavor Nambu-Jona-Lasinio model simulating Quantum Chromodynamics (QCD) at temperature $T$ and finite quark chemical potential $\mu$ without and with electrical neutrality (EN) condition and at any $T$ and $\mu$ without EN condition. By means of a quantitative investigation of the order parameter $m$, it is shown that a nonzero $M_0$ is bound to lead to nonzero quark-antiquark condensates throughout chiral phase transitions , no matter whether the order parameter $m$ varies discontinuously or continuously. In fact, a complete disappearance of the quark-antiquark condensates are proven to demand the non-physical and unrealistic conditions $\mu \,\geq$ or $\gg\, \sqrt{\Lambda^2+M_0^2}$ if $T=0$ and finite, or $T\to \infty$ if $\mu<\sqrt{\Lambda^2+M_0^2}$, where $\Lambda$ is the 3D momentum cut of the loop integrals. Theoretically these results show that when $M_0$ is included, we never have a complete restoration of dynamical (spontaneous) chiral symmetry breaking, including after a first order chiral phase transition at low $T$ and high $\mu$. In physical reality, it is the nonzero-ness of the quark-antiquark condensates that leads to the appearance of a critical end point in the first order phase transition line and the crossover behavior at high $T$ and/or high $\mu$ cases, rather than a possible tricritical point and a second order phase transition line. They also provide a basic reason for that one must consider the interplay between the chiral and diquark condensates in the research on color superconductor at zero $T$ and high $\mu$ case. The research shows that how a source term of the Lagrangian (at present i.e. the current quark mass term) can greatly affect dynamical behavior of a physical system.