We present the differential rates and branching ratios of the radiative decays τ→lννγ, with l = e or μ, and μ→eννγ 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(μ→eννγ) and B(τ→μννγ) for a minimum photon energy of 10 MeV in the μ and τ rest frames, respectively. Babar’s recent precise measurement of the branching ratio B(τ→eννγ), for the same photon energy threshold, differs from our prediction by 3.5 standard deviations.
