Pion superfluid phase transition at finite isospin chemical potential

TL;DR

This study investigates the pion superfluid phase transition at finite isospin chemical potential using Dyson-Schwinger equations, revealing phase boundaries and comparing results with lattice QCD data.

Contribution

It applies Dyson-Schwinger equations with rainbow truncation to analyze pion superfluidity at finite temperature and chemical potentials, providing new insights into phase boundaries.

Findings

Pion condensate remains zero below critical isospin chemical potential.

Results at T=113 MeV agree with lattice QCD data.

Pion superfluid phase appears at high isospin chemical potential and low temperature.

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, $\langle\pi\rangle$, as a function of $\mu_I$ at finite $T$ and $\mu_q$. At $T=(0, 80, 113, 120)$~MeV, the $\langle\pi\rangle$ keeps zero when $\mu_I$ is less than a critical value $\mu_{Ic}(T)$. The $\langle\pi\rangle$ 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 $\mu_q$, $\langle\pi\rangle$ 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.