Dispersive Analysis of $\omega/\phi \rightarrow 3\pi,\,\pi \gamma^*$

TL;DR

This paper employs a dispersive approach to analyze the decays of omega and phi mesons into three pions and their electromagnetic transition form factors, highlighting the significance of final state interactions.

Contribution

It introduces a dispersive framework with isobar decomposition and conformal mapping to accurately model decay amplitudes and form factors, accounting for inelastic effects.

Findings

Final state interactions can be sizable in these decays.

The formalism successfully describes Dalitz plot distributions.

Computed electromagnetic transition form factors for omega and phi decays.

Abstract

The decays $\omega/\phi \rightarrow 3\pi$ are considered in the dispersive framework that is based on the isobar decomposition and sub-energy unitarity. The inelastic contributions are parametrized by the power series in a suitably chosen conformal variable that properly accounts for the analytic properties of the amplitude. The Dalitz plot distributions and integrated decay widths are presented. Our results indicate that the final state interactions may be sizable. As a further application of the formalism we also compute the electromagnetic transition form factors of $\omega/\phi \rightarrow \pi^0\gamma^*$.