Influence of current mass on the spatially inhomogeneous chiral condensate

TL;DR

This study investigates how finite current quark mass influences the formation of spatially inhomogeneous chiral condensates in the NJL model at finite density, revealing that inhomogeneity persists despite the mass.

Contribution

It demonstrates that spatially inhomogeneous chiral condensates can exist even with finite current quark mass, extending previous massless analyses within the NJL model.

Findings

Inhomogeneous chiral condensates occur with finite quark mass.

Finite mass introduces competing effects on the condensate.

Baryon density becomes spatially inhomogeneous when condensates are inhomogeneous.

Abstract

It is known that, in the chiral limit, spatially inhomogeneous chiral condensate occurs in the Nambu-Jona-Lasinio (NJL) model at finite density within a mean-field approximation. We study here how an introduction of current quark mass affects the ground state with the spatially inhomogeneous chiral condensate. Numerical calculations show that, even if the current quark mass is introduced, the spatially inhomogeneous chiral condensate can take place. In order to obtain the ground state, the thermodynamic potential is calculated with a mean-field approximation. The influence of finite current mass on the thermodynamic potential consists of following two parts. One is a part coming from the field energy of the condensate, which favors inhomogeneous chiral condensate. The other is a part coming from the Dirac sea and the Fermi sea, which favors homogeneous chiral condensate. We also find that when the spatially inhomogeneous chiral condensate occurs, the baryon number density becomes spatially inhomogeneous.