Radiative μ and τ leptonic decays at NLO

A bstract We present the differential rates and branching ratios of the radiative decays $$ \tau \to l\overline{\nu}\nu \gamma $$ τ → l ν ¯ ν γ , with l = e or μ , and $$ \mu \to e\overline{\nu}\nu \gamma $$ μ → e ν ¯ ν γ 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 $$ \mathrm{\mathcal{B}}\left(\mu \to e\overline{\nu}\nu \gamma \right) $$ ℬ μ → e ν ¯ ν γ and $$ \mathrm{\mathcal{B}}\left(\tau \to \mu \overline{\nu}\nu \gamma \right) $$ ℬ τ → μ ν ¯ ν γ for a minimum photon energy of 10 MeV in the μ and τ rest frames, respectively. B abar ’s recent precise measurement of the branching ratio $$ \mathrm{\mathcal{B}}\left(\tau \to e\overline{\nu}\nu \gamma \right) $$ ℬ τ → e ν ¯ ν γ , for the same photon energy threshold, differs from our prediction by 3.5 standard deviations.