Quark-mass dependence in \(\omega \rightarrow 3\pi \) decays

We study the quark-mass dependence of \(\omega \rightarrow 3\pi \) 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 \(\omega \rightarrow 3\pi \) can serve as a paradigm case.