A microscopic study of pion condensation within Nambu--Jona-Lasinio model

TL;DR

This paper investigates pion condensation in neutral quark matter using the NJL model, revealing the conditions for its onset and its fragility due to explicit chiral symmetry breaking.

Contribution

It provides a microscopic analysis of pion condensation in quark matter, emphasizing the role of the electric chemical potential and quark mass in the NJL framework.

Findings

Pion condensation occurs when the electric chemical potential reaches the in-medium pion mass.

The transition to the condensed phase is second order under certain conditions.

Finite quark mass makes pion condensation highly fragile.

Abstract

We have studied the phenomenology of pion condensation in 2-flavor neutral quark matter at finite density with Nambu--Jona-Lasinio (NJL) model of QCD. We have discussed the role of the bare quark mass $m$ and the electric chemical potential $\mu_{e}$ in controlling the condensation. The central result of this work is that the onset for $\pi$-condensed phase occurs when $|\mu_{e}|$ reaches the value of the in-medium pion mass $M_{\pi}$ provided the transition is of the second order, even for a composite pion system in the medium. Finally, we have shown that the condensation is extremely fragile with respect to the explicit chiral symmetry breaking via a finite current quark mass.