Finite-Width Corrections to the Vector-Meson-Dominance Prediction forρ→e+e−

Abstract

Finite-width corrections based on a generalized effective range formula for pion-pion scattering modify by a non-negligible amount the well-known relation between $\ensuremath{\Gamma}(\ensuremath{\rho}\ensuremath{\rightarrow}{e}^{+}{e}^{\ensuremath{-}})$ and $\ensuremath{\Gamma}(\ensuremath{\rho}\ensuremath{\rightarrow}\ensuremath{\pi}\ensuremath{\pi})$ derived on the basis of vector-meson dominance. We also present a new current-algebra prediction for the shape and magnitude of $\ensuremath{\sigma}({e}^{+}{e}^{\ensuremath{-}}\ensuremath{\rightarrow}{\ensuremath{\pi}}^{+}{\ensuremath{\pi}}^{\ensuremath{-}})$ and estimate the $\ensuremath{\rho}$-meson contribution to the Schwinger term.