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

TL;DR

This paper studies the three-flavor Nambu--Jona-Lasinio model with the U_A(1) anomaly at finite isospin chemical potential, analyzing phase transitions, meson spectra, and topological susceptibility, highlighting the role of strangeness and anomaly effects.

Contribution

It extends the two-flavor models by including strangeness and the U_A(1) anomaly, providing a systematic analysis of mesonic excitations and topological susceptibility at finite isospin chemical potential.

Findings

Phase transition to pion superfluid occurs at  equal to the pion mass.

Strangeness effects are small in the pion superfluid phase.

Isospin density enhances topological susceptibility.

Abstract

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 $m_\pi$. Due to the U$_{\rm A}(1)$ anomaly, the strangeness degree of freedom couples to the light quark degrees of freedom and the strange quark effective mass depends on the pion condensate. However, the strange quark condensate and the strange quark effective mass change slightly in the pion superfluid phase, which verifies the validity of the two-flavor models. The effective four-fermion interaction of the Kobayashi-Maskawa-'t Hooft term in the presence of the pion condensation is constructed. Due to the U$_{\rm A}(1)$ anomaly, the pion condensation generally induces scalar-pseudoscalar interaction. The Bethe-Salpeter equation for the mesonic excitations is established and the meson mass spectra are obtained at finite isospin chemical potential and temperature. Finally, the general expression for the topological susceptibility $\chi$ at finite isospin chemical potential $\mu_{\rm I}$ is derived. In contrast to the finite temperature effect which suppresses $\chi$, the isospin density effect leads to an enhancement of $\chi$.