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

In this article we study the restoration of chiral symmetry at a finite temperature for quark matter with a chiral chemical potential, mu(5), by means of a nonlocal Nambu-Jona-Lasinio model. This model allows the introduction of, 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 the asymptotic behaviour expected in quantum chromodynamics in the 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.