Quark-mass dependence in ω→ 3 π decays

Abstract

We study the quark-mass dependence of ω→ 3 π decays, based on a dispersion-theoretical framework. We rely on the quark-mass-dependent scattering phase shift for the pion–pion P-wave extracted from unitarized chiral perturbation theory. The dispersive representation then takes into account the final-state rescattering among all three pions. The described formalism may be used as an extrapolation tool for lattice QCD calculations of three-pion decays, for which ω→ 3 π can serve as a paradigm case.