Light scalar susceptibilities and the $\pi^0-\eta$ mixing

TL;DR

This paper analyzes light scalar susceptibilities at finite temperature within SU(3)-Chiral Perturbation Theory, highlighting the dominant role of $ ext{pi}^0- ext{eta}$ mixing in the infrared regime below the critical temperature.

Contribution

It provides a thermal analysis of scalar susceptibilities including isospin breaking effects, emphasizing the model-independent impact of $ ext{pi}^0- ext{eta}$ mixing on flavor susceptibilities.

Findings

Connected scalar susceptibility dominated by $ ext{pi}^0- ext{eta}$ mixing

Model-independent $ ext{O}( ext{epsilon}^0)$ corrections identified

Susceptibility behavior relevant below the critical temperature

Abstract

We have performed a thermal analysis of the light scalar susceptibilities in the context of SU(3)-Chiral Perturbation Theory to one loop taking into account the QCD source of isospin breaking (IB), i.e corrections coming from $m_u\neq m_d$. We find that the value of the connected scalar susceptibility in the infrared regime and below the critical temperature is entirely dominated by the $\pi^0-\eta$ mixing, which leads to model-independent $\mathcal{O}(\epsilon^0)$ corrections, where $\epsilon\sim m_d-m_u$, in the combination $\chi_{uu}-\chi_{ud}$ of flavour breaking susceptibilities.