The fate of pion condensation in quark matter: from the chiral limit to the physical pion mass

TL;DR

This paper investigates pion condensation in neutral quark matter using the NJL model, revealing the critical role of electric charge neutrality and quark mass, and showing the fragility of pion condensates to explicit symmetry breaking.

Contribution

It demonstrates the persistence of the $ ext{e}= ext{M}_{ ext{π}^-}$ threshold in pion condensation and shows the extreme sensitivity of pion condensates to quark mass effects.

Findings

The $ ext{e}= ext{M}_{ ext{π}^-}$ threshold remains valid for second-order transitions.

Pion condensates are highly fragile to quark mass, disappearing for masses above ~10 keV.

Pion condensation is strongly affected by electric charge neutrality and explicit symmetry breaking.

Abstract

We study aspects of the pion condensation in two-flavor neutral quark matter using the Nambu--Jona-Lasinio model of QCD at finite density. We investigate the role of electric charge neutrality, and explicit symmetry breaking via quark mass, both of which control the onset of the charged pion $(\pi^c)$ condensation. We show that the equality between the electric chemical potential and the in-medium pion mass, $\mu_{e}=M_{\pi^-}$, as a threshold, persists even for a composite pion system in the medium, provided the transition to the pion condensed phase is of the second order. Moreover, we find that the pion condensate in neutral quark matter is extremely fragile to the symmetry breaking effect via a current quark mass $m$, and is ruled out for $m$ larger than the order of 10 keV.