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

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 quark-meson model with vacuum fluctuations included. Vacuum fluctuations give a divergent contribution to the vacuum energy, so the latter has to be renormalized before computing physical quantities. The vacuum term is important for restoration of chiral symmetry at finite temperature and $\mu_5\neq0$, therefore we present several plausible renormalization schemes for the ultraviolet divergences at $\mu_5\neq0$. Then we compute the critical temperature as a function of $\mu_5$. The main result of our study is that the choice of a renormalization scheme affects the critical temperature; among the three renormalization schemes we investigate, there exists one in which the critical temperature increases with $\mu_5$, a result which has not been found before by chiral model studies and which is in qualitative agreement with recent lattice data as well as with studies based on Schwinger-Dyson equations and universality arguments.