Estimation of the cumulant $b_4$ and sextic self-coupling of the QCD axion at finite temperature and density

Abstract

The sixth-order cumulant $b_4$ of the QCD topological charge distribution and the axion's sextic self-coupling at finite temperature $T$ and baryon chemical potential $\mu$ are calculated within the two-flavor quark-meson (QM) model without and with the Polyakov-loop dynamics. The $b_4$ in the vacuum falls within the range predicted by lattice SU(3) pure-gauge simulations, and at large $T$ and/or $\mu$, it tends to a constant predicted by the dilute instanton gas approximation. Both $b_4$ and the axion's sextic self-coupling diverge at the QCD critical point and flip sign across the phase transition. The convergence of the fourth- and sixth-order Taylor expansions of the free energy as a function of the $\theta$ parameter is investigated via comparison with the full potential at the mean-field level.

Comments: 17 pages, 17 figures,