Radiative mu and tau leptonic decays at NLO

We present the differential rates and branching ratios of the radiative decays tau -> l nu nu gamma, with l = e or mu, and mu -> e nu nu gamma in the Standard Model at next-to-leading order. Radiative corrections are computed taking into account the full depencence on the mass m l of the final charged leptons, which is necessary for the correct determination of the branching ratios. Only partial agreement is found with previous calculations performed in the m(l) -> 0 limit. Our results agree with the measurements of the branching ratios B (mu -> e (nu) over bar nu gamma) and B (tau -> mu(nu) over bar nu gamma) for a minimum photon energy of 10MeV in the mu and tau rest frames, respectively. BABAR's recent precise measurement of the branching ratio B (tau -> e (nu) over bar nu gamma), for the same photon energy threshold, differs from our prediction by 3.5 standard deviations.