Radiative corrections in weak semi-leptonic processes at low energy: a two-step matching determination

We focus on the chiral Lagrangian couplings describing radiative corrections to weak semi-leptonic decays and relate them to the decay amplitude of a lepton, computed by Braaten and Li at one loop in the Standard Model. For this purpose, we follow a two-step procedure. A first matching, from the Standard Model to Fermi theory, yields a relevant set of counterterms. The latter are related to chiral couplings thanks to a second matching, from Fermi theory to the chiral Lagrangian, which is performed using the spurion method. We show that the chiral couplings of physical relevance obey integral representations in a closed form, expressed in terms of QCD chiral correlators and vertex functions. We deduce exact relations among the couplings, as well as numerical estimates which go beyond the usual log(MZ/Mρ) approximation. Work supported in part by the EU RTN contract HPRN-CT-2002-00311 (EURIDICE). LPT is an unité mixte de recherche du CNRS et de l’Université Paris-Sud 11 (UMR 8627). IPN is an unité mixte de recherche du CNRS et de l’Université Paris-Sud 11 (UMR 8608).