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 (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 ${\eta }^{\prime }$ 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 $U_A(1)$ restoration takes place at 1.75 $T_c^{\chi }$=275 MeV.

arXiv comment20 pages, 14 figures. arXiv admin note: text overlap with arXiv:1301.3717

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