Pion superfluid phase transition at finite isospin chemical potential

Abstract

The pion superfluidity phase transition at $T-{\mu }_I$ and ${\mu }_q-{\mu }_I$ planes are studied in the framework of Dyson-Schwinger equations. The rainbow truncation and Gaussian effective gluon propagator are employed to calculate pion condensate, $⟨\pi ⟩$, as a function of ${\mu }_I$ at finite $T$ and ${\mu }_q$. At $T=(0,80,113,120)$~MeV, the $⟨\pi ⟩$ keeps zero when ${\mu }_I$ is less than a critical value ${\mu }_{Ic}(T)$. The $⟨\pi ⟩$ at $T=113$~MeV agrees with the lattice QCD result. At the $T-{\mu }_I$ plane, the pion superfluid phase appears at low temperature and high isospin chemical potential region. At finite ${\mu }_q$, $⟨\pi ⟩$ varying with ${\mu }_I$ almost coincide for ${\mu }_q<400$~MeV. At ${\mu }_q-{\mu }_I$ plane, the pion superfluid phase appears at ${\mu }_I\gtrsim m_{\pi }$ when ${\mu }_q<400$~MeV.

Comments: Online published in Eur. Phys. J. A (2021) 57:298