3-dimensional QCD phase diagram with pion condensate in the NJL model

TL;DR

This paper investigates the 3D QCD phase diagram with pion condensates using the NJL model, revealing phase transitions and the importance of accurate quark mass assumptions for reliable results.

Contribution

It provides a rigorous analysis of the pion condensate and phase transitions in the 3-flavor NJL model, incorporating lattice QCD data and isospin effects.

Findings

Identification of pion superfluid and Sarma phases at finite baryon chemical potential.

Phase transition types depend on temperature and chemical potential.

Incorrect assumptions about quark masses can significantly distort the phase diagram.

Abstract

With the isovector coupling constants adjusted to reproduce the physical pion mass and lattice QCD results in baryon-free quark matter, we have carried out rigourous calculations for the pion condensate in the 3-flavor Nambu-Jona-Lasinio model, and studied the 3-dimensional QCD phase diagram. With the increasing isospin chemical potential $\mu_I$, we have observed two nonzero solutions of the pion condensate at finite baryon chemical potentials $\mu_B$, representing respectively the pion superfluid phase and the Sarma phase, and their appearance and disappearance correspond to a second-order (first-order) phase transition at higher (lower) temperatures $T$ and lower (higher) $\mu_B$. Calculations by assuming equal constituent mass of $u$ and $d$ quarks would lead to large errors of the QCD phase diagram within $\mu_B \in (500, 900)$ MeV, and affect the position of the critical end point.