Scalar susceptibilities and Electromagnetic thermal mass differences in Chiral Perturbation Theory

TL;DR

This paper analyzes light scalar susceptibilities and electromagnetic thermal mass differences in Chiral Perturbation Theory, highlighting the dominant role of $b4-b7$ mixing in susceptibilities and the temperature dependence of pion mass splitting.

Contribution

It provides a thermal analysis of scalar susceptibilities including isospin breaking effects and calculates electromagnetic corrections to pion masses at finite temperature.

Findings

Connected scalar susceptibility dominated by $b4-b7$ mixing.

Mass splitting $M_{bcp^b1}-M_{bcp^0}$ increases with temperature.

Electromagnetic corrections to pion masses computed at next-to-leading order.

Abstract

We make a thermal analysis of the light scalar susceptibilities using SU(3)-Chiral Perturbation Theory to one loop taking into account the QCD source of isospin breaking (IB), i.e corrections coming from $m_u\neq m_d$. The value of the connected scalar susceptibility in the infrared regime, the one relevant when approaching chiral symmetry restoration, and below the critical temperature is found to be 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. We also present preliminary results for the corrections to the real part of the pion self-energy at nexst-to-leading order in SU(2)-Chiral Perturbation Theory taking into account electromagnetic interaction. The zero and finite temperature results for the charged and neutral pions are given in terms of the three-momentum of the external pion; and their difference is calculated to this order stressing the fact that, at low and moderate temperature, the mass splitting $M_{\pi^\pm}-M_{\pi^0}$ grows with temperature for, at least, non-zero charged pion mass running inside the loops.