Two-loop effective theory analysis of π(K)→e(ν)over-bare[γ] branching ratios

We study 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 two-loop effective theory results with a matching calculation of the counterterm, finding R(e/mu)((pi)) = (1.2352 +/- 0.0001) x 10(-4) and R(e/mu)((K)) = (2.477 +/- 0.001) x 10(-5).