Radiative corrections to radiative $\pi e2\mathrm{}$ decay

The lowest order radiative corrections to the width and spectra of the radiative $\pi e2\mathrm{}$ decay are calculated. We take into account the virtual photon emission contribution as well as soft and hard real photon emission contributions. The result turns out to be consistent with the standard Drell-Yan picture for the width and spectra in the leading logarithmical approximation which permits us to generalize it to all orders of perturbation theory. Explicit expressions of nonleading contributions are obtained. The contribution of the short distance is found to be in agreement with standard model predictions. It is presented as a general normalization factor. We check the validity of the Kinoshita-Lee-Nauenberg theorem about the cancellation in the total width of the mass singularities at the zero limit of the electron mass. We discuss the results of the previous papers devoted to this problem. The Dalitz plot distribution is illustrated numerically.