Radiative Tail in $\pi_{e2}$ Decay and Some Comments on $\mu-e$ Universality

Abstract

The result of lowest-order perturbation theory calculations of the photon and positron spectra in radiative pion(e2) decay are generalized to all orders of perturbation theory using the structure-function method. An additional source of radiative corrections to the ratio of the positron and muon channels of pion decay, due to emission of virtual and real photons and pairs, is considered. It depends on details of the detection of the final particles and is large enough to be taken into account in theoretical estimates with a level of accuracy of 0.1%.