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We calculate the ratios R_{e/mu}^{(P)} = Gamma(P -> e nu)/Gamma (P -> mu nu)(P=pi,K) in Chiral Perturbation Theory to order e^2 p^4. We complement the one-and two-loop effective theory results with a matching calculation of the localcounterterm, performed within the large-$N_C$ expansion. We findR_{e/mu}^{(\pi)} = (1.2352 \pm 0.0001)*10^{-4} and R_{e/mu}^{(K)} = (2.477 \pm0.001)*10^{-5}, with uncertainty induced by the matching procedure and chiralpower counting. Given the sensitivity of upcoming new measurements, our resultsprovide a clean baseline to detect or constrain effects from weak-scale newphysics in these rare decays. As a by-product, we also update the theoreticalanalysis of the individual pi/K -> \ell nu modes.

pi/K -> e nu branching ratios to O(e^2 p^4) in Chiral Perturbation Theory