Radiative $\mu$ and $\tau$ leptonic decays at NLO

Understand

We present the differential rates and branching ratios of the radiative decays $\tau \to l \bar{\nu} \nu \gamma$, with $l=e$ or $\mu$, and $\mu \to e \bar{\nu} \nu \gamma$ 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 $m_l \to 0$ limit.
• Our results agree with the measurements of the branching ratios $\mathcal{B} (\mu \to e \bar{\nu} \nu \gamma)$ and $\mathcal{B} (\tau \to \mu \bar{\nu} \nu \gamma)$ for a minimum photon energy of 10 MeV in the $\mu$ and $\tau$ rest frames, respectively.