Influence of current mass on the spatially inhomogeneous chiral condensate

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.