Radiative corrections to the decays K{sub L}{sup 0} {r_arrow} e{sup +}e{sup {minus}} and K{sub L}{sup 0} {r_arrow} {mu}{sup +} {mu}{sup {minus}}

The authors calculate the rates and lepton ({ell}) invariant mass distributions for decays of the form 0{sup {minus}+} {r_arrow} {ell}{sup +}{ell}{sup {minus}}{gamma}, which are important radiative corrections to the purely leptonic decays 0{sup {minus}+} {r_arrow} {ell}{sup +}{ell}{sup {minus}}. The approach uses the loop diagrams which arise by including the two photon intermediate state and they retain the imaginary parts of the loops--a radiative extension of the unitarity bound for the process. These results are compared with those obtained using a model in which the meson couples directly to the leptons