Light scalar susceptibilities and the $π^0-η$ mixing

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 $π^0-η$ mixing, which leads to model-independent $\mathcal{O}(ε^0)$ corrections, where $ε\sim m_d-m_u$, in the combination $χ_{uu}-χ_{ud}$ of flavour breaking susceptibilities.

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