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

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 $μ_{e}$ in controlling the condensation. The central result of this work is that the onset for $π$-condensed phase occurs when $|μ_{e}|$ reaches the value of the in-medium pion mass $M_π$ 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.