Exploring axial U(1) restoration in a modified 2+1 flavor Polyakov–quark–meson model

Abstract

We report on the $U_{A}(1)$ symmetry restoration resulting due to temperature dependence of the coefficient c(T) for the Kobayashi–Maskawa–’t Hooft determinant (KMT) term in a modified $2+1$ flavor Polyakov loop quark–meson model having fermionic vacuum correction term. Temperature dependence of KMT coupling c(T) drives the nonstrange condensate melting to significantly smaller temperatures in comparison with the constant c case. Further due to c(T), $m_{\eta ^{\prime }}$ decreases from its vacuum value by 220 MeV near $T=176$ MeV after the chiral transition ($T_{c}^{\chi }=154.9$ MeV). This is similar to the $\eta ^{\prime }$ in-medium mass drop of at least 200 MeV as reported by Csorgo and Vertesi in Ref (Phys Rev Lett 105:182301, 2010; Phys Rev C 83:054903 2011), as an experimental signature of the effective restoration of $U_A(1)$ symmetry. The pseudoscalar mixing angle $\theta _p$ achieves anti-ideal mixing in the influence of c(T). The $\eta$ meson becomes light quark system ($\eta _{NS}$) at $T=176$ MeV and changes its identity with $\eta '$ meson which becomes strange quark system ($\eta _{S}$). The degenerated temperature variations of $\sigma$, $\pi$ meson masses merges with the temperature variations of the masses of degenerated $a_{0}$, $\eta$ mesons near 275 MeV. It means that for c(T) when $m_{\sigma }=400$ MeV, the $U_{A}(1)$ restoration takes place at 1.75 $T_{c}^{\chi }=275$ MeV.