Thermal properties of $π$ and $ρ$ meson

We computed the pole masses and decay constants of $π$ and $ρ$ meson at finite temperature in the framework of Dyson-Schwinger equations and Bethe-Salpeter equations approach. Below transition temperature, pion pole mass increases monotonously, while $ρ$ meson seems to be temperature independent. Above transition temperature, pion mass approaches the free field limit, whereas $ρ$ meson is about twice as large as that limit. Pion and the longitudinal projection of $ρ$ meson decay constants have similar behaviour as the order parameter of chiral symmetry, whereas the transverse projection of $ρ$ meson decay constant rises monotonously as temperature increases. The inflection point of decay constant and the chiral susceptibility get the same phase transition temperature. Though there is no access to the thermal width of mesons within this scheme, it is discussed by analyzing the Gell-Mann-Oakes-Renner (GMOR) relation in medium. These thermal properties of hadron observables will help us understand the QCD phases at finite temperature and can be employed to improve the experimental data analysis and heavy ion collision simulations.

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