https://doi.org/10.1140/epjc/s2002-01072-7
theoretical physics
Radiative corrections to the 
decay revised
1
Bogoliubov Laboratory of Theoretical Physics, JINR, 141980, Dubna, Moscow region, Russia
2
Department of Physics and Astronomy, University of Pittsburgh, PA, USA
Received:
3
October
2002
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
