Radiative corrections to K3 decays

We have calculated the radiative corrections to the Dalitz plot for K3 and K30 decays, assuming a phenomenological weak K- vertex and using perturbation theory. The answer depends logarithmically on a cutoff. We have evaluated all terms which contribute to order analytically, without any approximations concerning the smallness of the muon mass or the "real inner bremsstrahlung." Thus, the dependence on the parameter (the ratio of the form factor f-f+) is exact. The radiative corrections to the K30 Dalitz plot, muon spectrum, and lifetime average around 2% over most of their respective ranges and are not especially sensitive to the cutoff. The radiative corrections to K3 decays is a fraction of a percent over most of the Dalitz plot and is sensitive to the cutoff. The radiative correction to the I=12 rule prediction for the ratio of the charged and neutral decay rates is approximately 2%. The final-state Coulomb correction accounts for most of this numerical result, the rest being model-dependent noise.