Three-flavor Nambu--Jona-Lasinio model at finite isospin chemical potential

Understand

QCD at finite isospin chemical potential $\mu_{\text I}$ possesses a positively definite fermion determinant and the lattice simulation can be successfully performed.

• While the two-flavor effective models may be sufficient to describe the phenomenon of pion condensation, it is interesting to study the roles of the strangeness degree of freedom and the U$_{\rm A}(1)$ anomaly.
• In this paper, we present a systematic study of the three-flavor Nambu--Jona-Lasinio model with a Kobayashi-Maskawa-'t Hooft (KMT) term that mimics the U$_{\rm A}(1)$ anomaly at finite isospin chemical potential.
• In the mean-field approximation, the model predicts a phase transition from the vacuum to the pion superfluid phase, which takes place at $\mu_{\rm I}$ equal to the pion mass $m_\pi$.