Radiative corrections in Kℓ30 decays

We calculate the long-distance radiative corrections δLDe and δLDμ to the K0 → π−e+νe and the K0 → π−μ+νμ decay rates. This analysis includes contributions to the long-distance radiative corrections from outside the kinematically allowed three-body Dalitz region and tests the sensitivity of the radiative corrections to the hadronic K-π form factors. A program, KLOR, was written to numerically evaluate the radiative corrections and to generate Monte Carlo events for experimental acceptance studies. The Ke30 and the Kμ30 long-distance radiative correction parameters are determined to be (1.3 ± 0.3)% and (1.9 ± 0.3)%, respectively. We also present predictions for the fraction of radiative Kℓ30 events satisfying various requirements on final-state photon kinematics.