Radiative Corrections toKl3±Decays

Abstract

The radiative corrections to the lepton spectrum and decay rate for ${K_{l3\mathrm{}}}^{\pm }$ decays are calculated, assuming a phenomenological weak $K-\pi$ vertex and using perturbation theory. The answer depends logarithmically on a cutoff. The result applied to pion beta decay yields a fractional change in lifetime of -1.2% and is not sensitive to reasonable variations in the cutoff. The radiative correction to the electron spectrum from ${K_{e3\mathrm{}}}^{\pm }$ decays at rest is substantial, averaging about 5% in absolute magnitude over most of the measurable energy range, and is insensitive to the cutoff. The correction to the ${K_{e3\mathrm{}}}^{\pm }$ lifetime, the ${K_{\mu 3}}^{\pm }$ lifetime and muon spectrum is probably small (a fraction of a percent) although the numerical estimates are sensitive to the cutoff.