Quark-mass dependence in $\omega \to 3\pi$ decays

We study the quark-mass dependence of $\omega \to 3\pi$ 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 $\omega \to 3\pi$ can serve as a paradigm case.