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Radiative Corrections to $π_{l2}$ and $K_{l2}$ Decays

We reexamine radiative corrections to $π_{l2}$ and $K_{l2}$ decays. We perform a matching calculation, including vector and axial vector resonances as explicit degrees of freedom in the long distance part. By considering the dependence on the matching scale and on the hadronic parameters, and by comparing with model independent estimates, we scrutinize the model dependence of the results. For the pseudoscalar meson decay constants, we extract the values f_pi = (92.1 \pm 0.3) MeV and f_K = (112.4 \pm 0.9) MeV. For the ratios R_pi and R_K of the electronic and muonic decay modes, we predict R_pi = (1.2354 \pm 0.0002) 10^{-4} and R_K = (2.472 \pm 0.001) 10^{-5}.