The branching ratio $\omega \to \pi^+\pi^-$ revisited

TL;DR

This paper revisits the omega to pion-pion branching ratio using dispersion theory, updating previous results, identifying data inconsistencies, and improving the pion charge radius estimate, with implications for related decay processes.

Contribution

It provides a model-independent analysis of recent data, refines the omega decay branching ratio, and improves the pion charge radius measurement, highlighting data inconsistencies and potential for future precision.

Findings

Updated omega to pion-pion branching ratio: (1.46±0.08)×10^{-2}

Improved pion charge radius: 0.6603(5)(4) fm

Modern eta' decay data can further refine transition strength

Abstract

We analyze the most recent data for the pion vector form factor in the timelike region, employing a model-independent approach based on dispersion theory. We confirm earlier observations about the inconsistency of different modern high-precision data sets. Excluding the BaBar data, we find an updated value for the isospin-violating branching ratio $\mathcal{B}(\omega \to \pi^+\pi^-) = (1.46\pm 0.08) \times 10^{-2}$. As a side result, we also extract an improved value for the pion vector or charge radius, $\sqrt{\langle r_V^2\rangle} = 0.6603(5)(4)\text{fm}$, where the first uncertainty is statistical as derived from the fit, while the second estimates the possible size of nonuniversal radiative corrections. In addition, we demonstrate that modern high-quality data for the decay $\eta' \to \pi^+\pi^-\gamma$ will allow for an even improved determination of the transition strength $\omega\to\pi^+\pi^-$.