Proper time regularization at finite quark chemical potential

Abstract

In this paper, we use the two-flavor Nambu–Jona-Lasinio (NJL) model to study the quantum chromodynamics (QCD) chiral phase transition. To deal with the ultraviolet (UV) issue, we adopt the popular proper time regularization (PTR), which is commonly used not only for hadron physics but also for the studies with magnetic fields. This regularization scheme can introduce the infrared (IR) cutoff to include quark confinement. We generalize the PTR to zero temperature and finite chemical potential case use a completely new method, and then study the chiral susceptibility, both in the chiral limit case and with finite current quark mass. The chiral phase transition is second-order in [Formula: see text] and [Formula: see text] and crossover at [Formula: see text] and [Formula: see text]. Three sets of parameters are used to make sure that the results do not depend on the parameter choice.