Topological susceptibility, divergent chiral density and phase diagram of chirally imbalanced QCD medium at finite temperature

We show that the nonlocal two-flavor Nambu-Jona-Lasinio model predicts the enhancement of both chiral and axial symmetry breaking as the chiral imbalance of hot QCD matter, regulated by a chiral chemical potential mu(5), increases. The two crossovers are reasonably close to each other in the range of mu(5) examined here, and the pseudocritical temperatures rise with mu(5). The curvatures of the chiral and axial crossovers for the chiral quark chemical potential approximately coincide and give kappa(5) similar or equal to -0.011. We point out that the presence of mu(5) in thermodynamic equilibrium is inconsistent with the fact that the chiral charge is not a Noether-conserved quantity for massive fermions. The chiral chemical potential should not, therefore, be considered as a true chemical potential that sets a thermodynamically stable environment in the massive theory, but rather as a new coupling that may require a renormalization in the ultraviolet domain. The divergence of an unrenormalized chiral density, coming from zero-point fermionic fluctuations, is a consequence of this property. We propose a solution to this problem via a renormalization procedure.