Three-dimensional QCD phase diagram with a pion condensate in the NJL model
Lu-Meng Liu, Jun Xu, Guang-Xiong Peng
Abstract
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 ${\ensuremath{\mu}}_{I}$, we have observed two nonzero solutions of the pion condensate at finite baryon chemical potentials ${\ensuremath{\mu}}_{B}$, 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) ${\ensuremath{\mu}}_{B}$. Calculations by assuming equal constituent mass of $u$ and $d$ quarks would lead to large errors of the QCD phase diagram within ${\ensuremath{\mu}}_{B}\ensuremath{\in}(500,900)\text{ }\text{ }\mathrm{MeV}$, and affect the position of the critical end point.