The branching ratio $\ddot{I}‰\to \ddot{I}{€}^{+}\ddot{I}{€}^{-}$ 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 $\mathcal{B}(\ddot{I}‰\to \ddot{I}{€}^{+}\ddot{I}{€}^{-})=(1.46\pm 0.08)\times 10^{-2}$. As a side result, we also extract an improved value for the pion vector or charge radius, $\sqrt{⟨r_V^2⟩}=0.6603(5)(4)\text{fm}$, 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 $\hat{I}{\cdot }^{\prime }\to \ddot{I}{€}^{+}\ddot{I}{€}^{-}{\hat{I}}^3$ will allow for an even improved determination of the transition strength $\ddot{I}‰\to \ddot{I}{€}^{+}\ddot{I}{€}^{-}$.

11+2 pages, 7+1 figures; v3: erratum appended that rectifies erroneous treatment of the BaBar data