The pionic beta decay in chiral perturbation theory

Abstract

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.

Improved estimates of rareKdecay matrix elements fromKℓ3decays

“…(10,13), are collected in Table 2. As explained in the text, there is at present an open question related to the isospin-breaking effects observed in the ratio of the K + ℓ3 form-factor over the K 0 ℓ3 one (see Eq.…”

“…These have been computed both restricting the K ℓ3γ phase-space to the three-body kinematics [12,13], and for the fully inclusive case [14,15].…”

“…[13] (which is based on the quark-mass analysis of Ref. [22] as well as from general dimensional analysis arguments for the K i counterterms).…”

Observations on the radiative corrections to pionβdecay

“…(11) It is also interesting to note that, more recently, the radiative corrections to pion β-decay have been studied in the framework of χPT [17]. In order to compare numerically the final result in that paper with ours, in Eq.…”

“…(5.4) of Ref. [17] we replace the shortdistance electroweak enhancement factor according to S EW (M ρ , M Z ) → 1 + (3α/2π) ln(Λ/M ρ ). In analogy with our Eq.…”