Radiative Corrections to theKe3±Dalitz Plot

The radiative corrections to the Dalitz plot in ${K_{e3\mathrm{}}}^{\pm }$ decays are calculated assuming a phenomenological weak $K-\pi$ vertex and using perturbation theory. The answer depends logarithmically on a cutoff, as is the case for nucleon $\beta$ decay. An interesting feature of these decays is that they offer a means of measuring the $q^2$ dependence of the form factors $f_{\pm }\left(q^2\right)$. The radiative corrections contribute an additional energy dependence to the measurements which cannot be separated experimentally. It is found that the radiative corrections are considerable, i.e., greater than 3% in absolute magnitude, over a large portion of the Dalitz plot, and are not particularly sensitive to a reasonable choice of cutoff.