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 $\Gamma (\rho \to e^{+}{e}^{-})$ and $\Gamma (\rho \to \pi \pi )$ derived on the basis of vector-meson dominance. We also present a new current-algebra prediction for the shape and magnitude of $\sigma (e^{+}{e}^{-}\to {\pi }^{+}{\pi }^{-})$ and estimate the $\rho$-meson contribution to the Schwinger term.