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

Abstract

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.

arXiv comment12 pages, 8 figures; v2: added two references, version published in EPJC

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• Multi-particle systems on the lattice and chiral extrapolations: a brief review
• Novel approaches in Hadron Spectroscopy
• Two-loop analysis of the pion-mass dependence of the $\rho$ meson
• Pole position of the $a_1(1260)$ resonance in a three-body unitary framework
• A phenomenological estimate of isospin breaking in hadronic vacuum polarization
• Towards an improved understanding of $\eta \to {\gamma }^{\ast }{\gamma }^{\ast }$
• Isospin-breaking effects in the three-pion contribution to hadronic vacuum polarization
• $\omega$ meson from lattice QCD
• The $\gamma \pi \to \pi \pi$ anomaly from lattice QCD and dispersion relations
• Chiral extrapolation of hadronic vacuum polarization
• Dispersion relation for hadronic light-by-light scattering: $\eta$ and ${\eta }^{\prime }$ poles
• What can we learn about light-meson interactions at electron-positron colliders?
• The electromagnetic form factors of the transition from the spin-3/2 Sigma to the Lambda hyperon
• Anomalous thresholds in $B\to (P,V){\gamma }^{\ast }$ form factors
• Analysis of rescattering effects in $3\pi$ final states
• Meson masses and decay constants in holographic QCD consistent with ChPT and HQET
• Advanced parametrisations for hadronic form factors
• Dispersive Analysis of $D$- and $B$-Meson Form Factors with Chiral and Heavy-Quark Constraints