Abstract
We study the quark-mass dependence of omega rightarrow 3pi 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 3pi can serve as a paradigm case.
Highlights
The described formalism may be used as an extrapolation tool for lattice Quantum Chromodynamics (QCD) calculations of three-pion decays, for which ω → 3π can serve as a paradigm case
Despite tremendous progress in simulating Quantum Chromodynamics (QCD) on space-time lattices using physical quark masses, many studies of complicated observables within lattice QCD are still performed with light quarks that are heavier than they are in the real world
The idea to employ dispersion theory to extend the applicability of inverse amplitude method (IAM)-generated phase shifts is not new: it has already been applied to describe the pion vector form factor [20], as well as, in a formalism closely related to what we present here, to the reaction γ π → π π [21]
Summary
Despite tremendous progress in simulating Quantum Chromodynamics (QCD) on space-time lattices using physical quark masses, many studies of complicated observables within lattice QCD are still performed with light quarks that are heavier than they are in the real world (see e.g. Refs. [1,2] for reviews). The IAM can be justified using dispersion theory; scattering amplitudes constructed via the IAM match smoothly on the ChPT expansion at low energies. In this manner, the properties of elastic resonances such as the f0(500). Pion two-body phase shift as input, which we extract from the known quark-mass-dependent IAM partial wave. The idea to employ dispersion theory to extend the applicability of IAM-generated phase shifts is not new: it has already been applied to describe the pion vector form factor [20], as well as, in a formalism closely related to what we present here, to the reaction γ π → π π [21].
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
