Radiative corrections to the decay revised
Bogoliubov Laboratory of Theoretical Physics, JINR, 141980, Dubna, Moscow region, Russia
2 Department of Physics and Astronomy, University of Pittsburgh, PA, USA
Published online: 24 January 2003
We consider the lowest order radiative corrections for the decay , usually referred to as decay. This decay is the best way to extract the value of the V us element of the CKM matrix. The radiative corrections become crucial if one wants a precise value of V us . The existing calculations were performed in the late 60’s and are in disagreement. The calculation by Ginsberg turns out to be ultraviolet cutoff sensitive. The necessity of precise knowledge of V us and the contradiction between the existing results constitute the motivation of our paper.
We remove the ultraviolet cutoff dependence by using Sirlin’s prescription; we set it equal to the W mass. We establish the whole character of the 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 . The corrected total width is with . Using the form factor value calculated by Cirigliano et al. leads to .
© Springer-Verlag Berlin/Heidelberg, 2003