ππ and πK scatterings in three-flavour resummed chiral perturbation theory

The (light but not-so-light) strange quark may play a special role in the low-energy dynamics of QCD. The presence of strange quark pairs in the sea may have a significant impact of the pattern of chiral symmetry breaking: in particular large differences can occur between the chiral limits of two and three massless flavours (i.e., whether ms is kept at its physical value or sent to zero). This may induce problems of convergence in three-flavour chiral expansions. To cope with such difficulties, we introduce a new framework, called Resummed Chiral Perturbation Theory. We exploit it to analyse ππ and πK scatterings and match them with dispersive results in a frequentist framework. Constraints on three-flavour chiral order parameters are derived.