QCD-inequality analyses on pion condensate at real and imaginary isospin chemical potentials under finite imaginary quark chemical potential

TL;DR

This paper uses QCD inequalities to analyze pion condensate formation under real and imaginary isospin chemical potentials, revealing conditions for condensation and evaluating neutral-pion expectations with implications for the Banks-Casher relation.

Contribution

It provides a novel analysis of pion condensates at finite imaginary and real chemical potentials using QCD inequalities and twisted mass framework.

Findings

Charged pion condenses at real isospin chemical potential.

No pion condensation occurs at imaginary isospin chemical potential.

Neutral-pion expectation value is zero at finite quark mass in the imaginary chemical potential regime.

Abstract

By employing QCD inequalities, we discuss appearance of the pion condensate for both real and imaginary isospin chemical potentials, taking also into account imaginary quark chemical potential. We show that the charged pion can condense for real isospin chemical potential, but not for imaginary one. Furthermore, we evaluate the expectation value of the neutral-pion field for imaginary isospin chemical potential by using framework of the twisted mass. As a result, it is found that the expectation value becomes zero for the finite current-quark mass, whereas the Banks-Casher relation is obtained in the massless limit.