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

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 η ′ decreases from its vacuum value by 220 MeV near T = 176 MeV after the chiral transition ( T c χ = 154.9 MeV). This is similar to the η ′ 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 θ p achieves anti-ideal mixing in the influence of c ( T ). The η meson becomes light quark system ( η NS ) at T = 176 MeV and changes its identity with η ′ meson which becomes strange quark system ( η S ). The degenerated temperature variations of σ , π meson masses merges with the temperature variations of the masses of degenerated a 0 , η mesons near 275 MeV. It means that for c ( T ) when m σ = 400 MeV, the U A ( 1 ) restoration takes place at 1.75 T c χ = 275 MeV.