Abstract
We present the differential rates and branching ratios of the radiative decays \( \tau \to l\overline{\nu}\nu \gamma \), with l = e or μ, and \( \mu \to e\overline{\nu}\nu \gamma \) in the Standard Model at next-to-leading order. Radiative corrections are computed taking into account the full depencence on the mass ml 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 ml → 0 limit. Our results agree with the measurements of the branching ratios \( \mathrm{\mathcal{B}}\left(\mu \to e\overline{\nu}\nu \gamma \right) \) and \( \mathrm{\mathcal{B}}\left(\tau \to \mu \overline{\nu}\nu \gamma \right) \) 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 \( \mathrm{\mathcal{B}}\left(\tau \to e\overline{\nu}\nu \gamma \right) \), for the same photon energy threshold, differs from our prediction by 3.5 standard deviations.
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Fael, M., Mercolli, L. & Passera, M. Radiative μ and τ leptonic decays at NLO. J. High Energ. Phys. 2015, 153 (2015). https://doi.org/10.1007/JHEP07(2015)153
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DOI: https://doi.org/10.1007/JHEP07(2015)153