Radiative corrections to the K sub e sub 3 sup+- decay revised

The lowest order radiative corrections for the decay K sup+- -> pi sup 0 e sup+- nu, usually referred as K sub e sub 3 sup+- decay, are considered. This decay is the best way to extract the value of the V sub u sub s element of the CKM matrix. The radiative corrections become crucial if one wants to get a precise value of V sub u sub s. The necessity of precise knowledge of V sub u sub s and the contradiction between the existing results constitute the motivation of our paper. We remove the ultraviolet cutoff dependence by using A. Sirlin's prescription; we set it equal to the W mass. We establish the whole character of small lepton mass dependence based on the renormalization group approach. In this way we can provide a simple explanation of Kinoshita-Lee-Nauenberg cancellation of singularities in the lepton mass terms in the total width and pion spectrum. We give an explicit evaluation of the structure-dependent photon emission based on ChPT in the lowest order. We estimate the accuracy of our results to be at the level of 1 %. The corrected total width is GAMMA = GAMMA sub 0 (1 + delta) with delta = 0.0200 +- 0.0002. The form factor value f sub + (0) = 0.9842 +- 0.0084 leads to |V sub u sub s sub | = 0.2172 +- 0.0055