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

TL;DR

This paper calculates the differential rates and branching ratios of radiative leptonic decays of muons and taus at NLO in the Standard Model, including full mass dependence, and compares results with experimental data.

Contribution

It provides the first complete NLO calculations with full mass dependence for these decays, improving accuracy over previous massless approximations.

Findings

Results agree with some experimental measurements for certain decays.

Discrepancy of 3.5 standard deviations with recent BaBar measurement for tau to electron decay.

Partial agreement with previous calculations in the massless limit.

Abstract

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. Babar's recent precise measurement of the branching ratio $\mathcal{B} (\tau \to e \bar{\nu} \nu \gamma)$, for the same photon energy threshold, differs from our prediction by 3.5 standard deviations.