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The branching fractions of radiative leptonic $\tau$ decays $(\tau \to l \nu\bar{\nu} \gamma$, $l=e,\mu)$ were recently measured by the Babar collaborationwith a relative error of about 3%. The measurement of the branching ratio$\mathcal{B} (\tau \to e \bar{\nu} \nu \gamma)$, for a minimum photon energy of10 MeV in the $\tau$ rest frame, differs from our recent SM prediction by 3.5standard deviations, whereas our result agrees with Babar's value for$\mathcal{B} (\tau \to \mu \bar{\nu} \nu \gamma)$. Our predictions also agreewith the measurement of $\mathcal{B} (\mu \to e \bar{\nu} \nu \gamma)$ by theMEG collaboration. We also report on a recent proposal to test the $\tau$dipole moments via precise measurements of radiative leptonic $\tau$ decays athigh-luminosity $B$ factories.

Precision tests via radiative $\mu$ and $\tau$ leptonic decays