π/K→e(ν)over-bare branching ratios to O(e2p4) in Chiral Perturbation Theory

We calculate the ratios R-e/mu((P)) equivalent to Gamma(P -> e (nu) over bar (e)[gamma])/Gamma (P -> mu(nu) over bar (mu)[gamma]) (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 local counterterm, performed within the large-Nc expansion. We find R-e/mu((pi)) (1.2352 +/- 0.0001) X 10(-4) and R-e/mu((K)) (2.477 +/- 0.001) x to-5, with uncertainty induced by the matching procedure and chiral power counting. Given the sensitivity of upcoming new measurements, our results provide a clean baseline to detect or constrain effects from weak-scale new physics in these rare decays. As a by-product, we also update the theoretical analysis of the individual pi(K)->(nu) over bar (l) modes.