Pion and $\eta$-meson mass splitting at the two-flavour chiral crossover

TL;DR

This paper investigates how the mass difference between pions and eta mesons evolves across the chiral crossover, using functional renormalization group methods and a Polyakov-quark-meson model to connect scale dependence to temperature effects.

Contribution

It introduces a novel approach combining RG scale dependence with a Polyakov-quark-meson model to study meson mass splitting at finite temperature.

Findings

The temperature dependence of the pion and eta meson mass splitting is quantitatively determined.

The 't Hooft determinant's role in meson mass splitting is elucidated across the chiral crossover.

Abstract

We study the splitting in the screening mass of pions and the $\eta$-meson across the chiral crossover. This splitting is determined by the 't Hooft determinant. We use results for the renormalisation group scale dependence of the 't Hooft determinant obtained within the functional renomalisation group in quenched QCD with two flavours. The scale dependence of the 't Hooft determinant is mapped to its temperature dependence with the help of a Polyakov-quark-meson model. As a result we obtain the temperature dependence of the splitting in the screening mass of pions and the $\eta$-meson.