Quark-mass dependence in $$\omega \rightarrow 3\pi $$ ω→3π decays

Abstract

Abstract We study the quark-mass dependence of $$\omega \rightarrow 3\pi $$ ω→3π 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 $$\omega \rightarrow 3\pi $$ ω→3π can serve as a paradigm case.