Radiative Corrections to the $K_{e3}^{\pm}$ Decay Revised

V. Bytev; E. Kuraev; A. Baratt; J. Thompson

doi:10.1140/epjc/s2002-01072-7

paper

Radiative Corrections to the $K_{e 3}^{\pm}$ Decay Revised

arXiv:hep-ph/0210049 · doi:10.1140/epjc/s2002-01072-7

Abstract

We consider the lowest order radiative corrections for the decay $K^{\pm} \to π^{0} e^{\pm} ν$ , usually referred as $K_{e 3}^{\pm}$ decay. This decay is the best way to extract the value of the $V_{u s}$ element of the CKM matrix. The radiative corrections become crucial if one wants a precise value of $V_{u s}$ . The existing calculations were performed in the late 60's \cite{B,G} and are in disagreement. The calculation in \cite{G} turns out to be ultraviolet cutoff sensitive. The necessity of precise knowledge of $V_{u s}$ 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 $Γ = Γ_{0} (1 + δ)$ with $δ = 0.02 \pm 0.0002$ . Using the formfactor value $f_{+} (0) = 0.9842 \pm 0.0084$ calculated in \cite{CKNRT} leads to $∣ V_{u s} ∣ = 0.2172 \pm 0.0055$ .

29 pages, 4 figures, 2 tables, uses feynmf.sty

Radiative Corrections to the Ke3±​ Decay Revised

Abstract

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Radiative Corrections to the $K_{e 3}^{\pm}$ Decay Revised