Kℓ3 form factors and strong superconvergence

Abstract

We discuss the superconvergence of a certain invariant amplitude and the corrections to the Weinberg sum rules due to nonvanishing pion and kaon masses. New sum rules for spectral functions are obtained. We apply these sum rules to calculate the Kl3 form factors and obtain ξ=−1.54 for λ+=0 and ξ=−1.05 for λ+=0.02. These values of ξ are nearly constant throughout the physical region. These results are in very good agreement with the data of the polarization experiment.