The branching ratio $$\omega \rightarrow \pi ^+\pi ^-$$ ω→π+π- revisited

Abstract

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 $${\mathscr {B}}(\omega \rightarrow \pi ^+\pi ^-) = (1.46\pm 0.08) \times 10^{-2}$$ B(ω→π+π-)=(1.46±0.08)×10-2 . As a side result, we also extract an improved value for the pion vector or charge radius, $$\sqrt{\langle r_V^2\rangle } = 0.6603(5)(4)\,\text {fm}$$ ⟨rV2⟩=0.6603(5)(4)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 $$\eta '\rightarrow \pi ^+\pi ^-\gamma $$ η′→π+π-γ will allow for an even improved determination of the transition strength $$\omega \rightarrow \pi ^+\pi ^-$$ ω→π+π- .