Light scalar susceptibilities and isospin breaking

Abstract

Making a thermal analysis in the context of NLO SU(3) Chiral Perturbation Theory we see that isospin breaking (1B) corrections (both electromagnetic and QCD ones) to quark condensates are of order beta(e(2)) and beta(epsilon) with epsilon the pi(0) - eta mixing angle. However the combination chi(uu) - chi(ud) of flavour breaking susceptibilities, which vanishes in the isospin limit and can be identified essentially with the connected susceptibility, has an order beta(1) contribution enhanced with T because of the pi 0 - eta mixing. Finally we present a thermal sum rule that relates quark condensate ratios and the light scalar susceptibility without IB, chi(T) - chi(0).