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.

我们报告了\（U_ {A}（1）\）对称性的恢复，这是由于在修改的\（2+中，小林-Maskawa-t Hooft行列式（KMT）项的系数c（T）与温度有关的1 \）具有Polyfkov真空校正项的味觉Polyakov环夸克-介子模型。与恒定c情况相比，KMT耦合c（T）的温度依赖性将非奇异的冷凝物熔化到更低的温度。此外，由于c（T），\（m _ {\ eta ^ {\ prime}} \） 在手性跃迁之后，在\（T = 176 \） MeV附近从其真空值降低了220 MeV 。\（T_ {c} ^ {\ chi} = 154.9 \）  MeV）。这类似于Csorgo和Vertesi在Ref（Phys Rev Lett 105：182301，2010; Phys Rev C 83：054903）中报道的\（\ eta ^ {\ prime} \）中等质量下降至少200 MeV 2011），作为\（U_A（1）\）对称性有效恢复的实验签名。伪标量混合角\（\ theta _p \）在c（T）的影响下实现了反理想混合。的\（\ ETA \）介子变轻夸克系统（\（\ ETA _ {NS} \） ）在\（T = 176 \）  MeV的并改变其与身份\（\ ETA'\）成为奇异夸克介子系统（\（\ eta _ {S} \））。退化的\（\ sigma \），\（\ pi \）介子质量的温度变化与退化的\（a_ {0} \），\（\ eta \）介子质量的温度变化合并在275 MeV附近。这意味着对于\（m _ {\ sigma} = 400 \）  MeV的c（T），\（U_ {A}（1）\）恢复发生在1.75 \（T_ {c} ^ {\ chi} = 275 \）  MeV。