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We study the ratios R_{e/mu}^{(P)} = Gamma(P -> e nu [gamma])/Gamma(P -> munu [gamma]) (P=pi,K) in Chiral Perturbation Theory to order e^2 p^4. Wecomplement the two-loop effective theory results with a matching calculation ofthe counterterm, finding R_{e/mu}^{(pi)} = (1.2352 \pm 0.0001)*10^(-4) andR_{e/mu}^{(K)} = (2.477 \pm 0.001)*10^(-5).

The Standard Model prediction for R_{e/mu}^{(pi,K)}