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

Understand

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.