We focus on the chiral Lagrangian couplings describing radiative correctionsto weak semi-leptonic decays and relate them to the decay amplitude of alepton, computed by Braaten and Li at one loop in the Standard Model. For thispurpose, we follow a two-step procedure. A first matching, from the StandardModel to Fermi theory, yields a relevant set of counterterms. The latter arerelated to chiral couplings thanks to a second matching, from Fermi theory tothe chiral Lagrangian, which is performed using the spurion method. We showthat the chiral couplings of physical relevance obey integral representationsin a closed form, expressed in terms of QCD chiral correlators and vertexfunctions. We deduce exact relations among the couplings, as well as numericalestimates which go beyond the usual $\log(M\_Z/M\_\rho)$ approximation.
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