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

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 $\omega\to\pi^+\pi^-$.