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

Abstract : 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 $\kappa_5 \simeq - 0.011$. 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 than as a new coupling that may require a renormalization in the ultraviolet domain. The divergence of an unrenormalized chiral density, \corr{coming from zero-point fermionic fluctuations,} is a consequence of this property. We propose a solution to this problem via a renormalization procedure.
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Marco Ruggieri, M. N. Chernodub, Zhen-Yan Lu. Topological susceptibility, divergent chiral density and phase diagram of chirally imbalanced QCD medium at finite temperature. Physical Review D, American Physical Society, 2020, 102, pp.014031. ⟨10.1103/PhysRevD.102.014031⟩. ⟨hal-02567809⟩

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