Meson Masses and Mixing Angles in 2+1 Flavor Polyakov Quark Meson Sigma Model and Symmetry Restoration Effects

TL;DR

This paper investigates how the inclusion of the Polyakov loop affects meson masses, mixing angles, and chiral symmetry restoration in a 2+1 flavor quark meson sigma model, revealing sharper symmetry restoration and early strange condensate melting.

Contribution

It introduces the Polyakov loop into the quark meson linear sigma model and analyzes its impact on meson properties and symmetry restoration, including the role of the axial anomaly.

Findings

Polyakov loop sharpens chiral symmetry restoration.

Early melting of strange condensate with Polyakov loop.

Altered convergence of meson chiral partners.

Abstract

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 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 ($\pi$, $\eta$, $\eta'$, $K$) and scalar ($\sigma$, $a_0$, $f_0$,$\kappa$) 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 ($\eta$ and $\eta'$) and scalar ($\sigma$ and $f_0$)meson complex, has also been investigated in the Polyakov 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.