We present a detailed numerical study of the K e3 decays to O(p 6 , (m d − m u )p 2 , e 2 p 2 ) in chiral perturbation theory with virtual photons and leptons. We describe the extraction of the CKM matrix element |V us | from the experimental K e3 decay parameters. We propose a consistency check of the K + e3 and K 0 e3 data that is largely insensitive to the dominating theoretical uncertainties, in particular the contributions of O(p 6 ). Our analysis is highly relevant in view of the recent high statistics measurement of the K + e3 branching ratio by E865 at Brookhaven which does not indicate any significant deviation from CKM unitarity but rather a discrepancy with the present K 0 e3 data.
Within the framework of chiral perturbation theory with virtual photons and leptons, we present an updated analysis of the pionic beta decay including all electromagnetic contributions of order e 2 p 2 . We discuss the extraction of the Cabibbo-Kobayashi-Maskawa matrix element |V ud | from experimental data. The method employed here is consistent with the analogous treatment of the K ℓ3 decays and the determination of |Vus|. PACS. 13.40.Ks Electromagnetic corrections to strong and weak-interaction processes -12.15.Hh Determination of Kobayashi-Maskawa matrix elements -12.39.Fe Chiral Lagrangians ⋆ Work supported in part by IHP-RTN, EC-Contract No. HPRN-CT-2002-00311 (EURIDICE).1 The two-loop expressions of the K ℓ3 form factors have been worked out in [7], but no evaluation of the relevant O(p 6 ) counterterms was given.
A reanalysis of the radiative pion decay together with the calculation of the radiative corrections within chiral perturbation theory (CHPT) is performed. The amplitude of this decay contains an inner Bremsstrahlung contribution and a structure-dependent part that are both accessible in experiments. In order to obtain a reliable estimate of the hadronic contributions we combine the CHPT result with a large-N C expansion and experimental data on other decays, which makes it possible to determine the occurring coupling constants.
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