Meson masses and mixing angles in the<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mn>2</mml:mn><mml:mo>+</mml:mo><mml:mn>1</mml:mn></mml:math>flavor Polyakov quark meson sigma model and symmetry restoration effects

The meson masses and mixing angles have been calculated for the scalar and pseudoscalar sector in the framework of the generalized $2+1$ flavor Polyakov loop augmented quark meson linear sigma model. We have given the results for two different forms of the effective Polyakov loop potential. The comparison of results with the existing calculations in the bare $2+1$ quark meson linear sigma model, shows that the restoration of chiral symmetry becomes sharper due to the influence of the Polyakov loop potential. We find that inclusion of the Polyakov loop in the quark meson linear sigma model together with the presence of axial anomaly, triggers an early and significant melting of the strange condensate. We have examined how the inclusion of the Polyakov loop qualitatively and quantitatively affects the convergence in the masses of the chiral partners in pseudoscalar ($\ensuremath{\pi}$, $\ensuremath{\eta}$, ${\ensuremath{\eta}}^{\ensuremath{'}}$, $K$) and scalar ($\ensuremath{\sigma}$, ${a}_{0}$, ${f}_{0}$, $\ensuremath{\kappa}$) meson nonets as the temperature is varied on the reduced temperature scale. The role of ${U}_{A}(1)$ anomaly in determining the isoscalar masses and mixing angles for the pseudoscalar ($\ensuremath{\eta}$ and ${\ensuremath{\eta}}^{\ensuremath{'}}$) and scalar ($\ensuremath{\sigma}$ and ${f}_{0}$) meson complex, has also been investigated in the Polyakov loop augmented quark meson linear sigma model. The interplay of chiral symmetry restoration effects and the setting up of ${U}_{A}(1)$ restoration trend has been discussed and analyzed in the framework of the presented model calculations.