pi-pi and pi-K scatterings in three-flavour resummed chiral perturbation theory

TL;DR

This paper introduces Resummed Chiral Perturbation Theory to analyze pi-pi and pi-K scatterings, addressing convergence issues in three-flavour chiral expansions caused by the strange quark's role in low-energy QCD dynamics.

Contribution

The paper presents a new resummation framework for chiral perturbation theory, improving analysis of meson scatterings involving the strange quark.

Findings

Constraints on three-flavour chiral order parameters derived.

Resummed Chiral Perturbation Theory matches dispersive results effectively.

Addresses convergence problems in three-flavour chiral expansions.

Abstract

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 m_s 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 pi-pi and pi-K scatterings and match them with dispersive results in a frequentist framework. Constraints on three-flavour chiral order parameters are derived.