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 three-flavor Nambu-Jona-Lasinio model, and studied the three-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 ${\mu }_B\in (500,900)\mathrm{MeV}$, and affect the position of the critical end point.

• Received 21 August 2021
• Accepted 14 September 2021

DOI:https://doi.org/10.1103/PhysRevD.104.076009

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Published by the American Physical Society