Inhomogeneous chiral phases away from the chiral limit

TL;DR

This paper investigates how explicit chiral-symmetry breaking affects inhomogeneous chiral phases using a Nambu-Jona-Lasinio model, revealing the persistence of inhomogeneous phases and the replacement of the critical endpoint by a pseudo-Lifshitz point.

Contribution

It generalizes previous chiral limit results to finite quark masses, showing the inhomogeneous phase's robustness and the nature of phase boundary instabilities.

Findings

Inhomogeneous phase persists at large quark masses.

Critical endpoint replaced by a pseudo-Lifshitz point.

Scalar modulations are favored over pseudoscalar ones.

Abstract

The effect of explicit chiral-symmetry breaking on inhomogeneous chiral phases is studied within a Nambu-Jona-Lasinio model with nonzero current quark mass. Generalizing an earlier result obtained in the chiral limit, we show within a Ginzburg-Landau analysis that the critical endpoint of the first-order chiral phase boundary between two homogeneous phases gets replaced by a "pseudo-Lifshitz point" when the possibility of inhomogeneous order parameters is considered. Performing a stability analysis we also show that the unstable mode along the phase boundary is in the scalar but not in the pseudoscalar channel, suggesting that modulations which contain pseudoscalar condensates, like a generalized dual chiral density wave, are disfavored against purely scalar ones. Numerically we find that the inhomogeneous phase shrinks as one moves away from the chiral limit, but survives even at significantly large values of the current quark mass.