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

We report on the $U_A\left(1\right)$ 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 $U_A\left(1\right)$ 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 ${\eta }^{\prime }$ 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 $U_A\left(1\right)$ restoration takes place at 1.75 $T_c^{\chi }=275$ MeV.