Quark-mass dependence in $\omega\to3\pi$ decays

TL;DR

This paper investigates how the decay process  dependence on quark mass using dispersion theory, aiding lattice QCD extrapolations.

Contribution

It introduces a dispersion-theoretical framework incorporating quark-mass-dependent phase shifts for analyzing  decays and providing a tool for lattice QCD extrapolations.

Findings

Framework accounts for final-state rescattering effects.

Can be used to extrapolate lattice QCD results.

Provides insights into quark-mass dependence of decay processes.

Abstract

We study the quark-mass dependence of $\omega\to3\pi$ 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 $\omega\to3\pi$ can serve as a paradigm case.