Mesonic excitations and pi--pi scattering lengths at finite temperature in the two-flavor Polyakov--Nambu--Jona-Lasinio model

TL;DR

This paper investigates mesonic excitations and pi--pi scattering lengths at finite temperature using the two-flavor PNJL model, highlighting the effects of color confinement and extending key relations to finite temperature.

Contribution

It introduces finite-temperature calculations of mesonic properties and scattering lengths within the PNJL model, comparing different effective potentials and extending fundamental relations.

Findings

Results are nearly independent of the Polyakov-loop potential choice.

Color confinement effects screen temperature effects below the critical temperature.

Key relations are extended to finite temperature in the PNJL framework.

Abstract

The mesonic excitations and s-wave pi--pi scattering lengths at finite temperature are studied in the two-flavor Polyakov--Nambu--Jona-Lasinio (PNJL) model. The masses of pi-meson and sigma-meson, pion-decay constant, the pion-quark coupling strength, and the scattering lengths $a_{0}$ and $a_{2}$ at finite temperature are calculated in the PNJL model with two forms of Polyakov-loop effective potential. The obtained results are almost independent of the choice of the effective potentials. The calculated results in the PNJL model are also compared with those in the conventional Nambu--Jona-Lasinio model and indicate that the effect of color confinement screens the effect of temperature below the critical one in the PNJL model. Furthermore, the Goldberger-Treiman relation and the Gell-Mann--Oakes--Renner relation are extended to the case at finite temperature in the PNJL model.