Radiative corrections in weak semi-leptonic processes at low energy: a two-step matching determination*
Laboratoire de Physique Théorique, Université Paris-Sud 11, 91406, Orsay, France
2 Institut de Physique Nucléaire, Université Paris-Sud 11, 91406, Orsay, France
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 approximation.
© Springer-Verlag, 2005