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

## TL;DR

This paper investigates how temperature-dependent axial U(1) symmetry restoration occurs in a modified 2+1 flavor Polyakov quark meson model, showing significant effects on meson masses and mixing angles near the chiral transition.

## Contribution

It introduces a temperature-dependent Kobayashi-Maskawa-'t Hooft determinant term in the model, revealing novel insights into U(1) symmetry restoration and meson behavior at high temperatures.

## Key findings

- Significant decrease in $ ext{m}_{ ext{η}'}$ mass near T=176 MeV.
- U(1) symmetry restoration occurs at approximately 1.75 times the chiral transition temperature.
- Meson mass degeneracy and mixing angle changes indicate effective symmetry restoration.

## 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 (PQMVT).Temperature dependence of KMT coupling c(T) drives the non-strange condensate melting to significantly smaller temperatures in comparison to 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.