Critical Temperature of Chiral Symmetry Restoration for Quark Matter with a Chiral Chemical Potential

Abstract

In this article we study restoration of chiral symmetry at finite temperature for quark matter with a chiral chemical potential, ${\mu }_5$, by means of a nonlocal Nambu-Jona-Lasinio model. This model allows to introduce in the simplest way possible a Euclidean momentum, $p_E$, dependent quark mass function which decays (neglecting logarithms) as $1/p_E^2$ for large $p_E$, in agreement with asymptotic behaviour expected in QCD in presence of a nonperturbative quark condensate. We focus on the critical temperature for chiral symmetry restoration in the chiral limit, $T_c$, versus ${\mu }_5$, as well as on the order of the phase transition. We find that $T_c$ increases with ${\mu }_5$, and that the transition remains of the second order for the whole range of ${\mu }_5$ considered.

Comments: Section 3.2 added. To appear on Journal of Physics G