  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 $\log(M\_Z/M\_\rho)$ approximation.
