Precision tests via radiative $μ$ and $τ$ leptonic decays

The branching fractions of radiative leptonic $τ$ decays $(τ\to l ν\barν γ$, $l=e,μ)$ were recently measured by the Babar collaboration with a relative error of about 3%. The measurement of the branching ratio $\mathcal{B} (τ\to e \barν νγ)$, for a minimum photon energy of 10 MeV in the $τ$ rest frame, differs from our recent SM prediction by 3.5 standard deviations, whereas our result agrees with Babar's value for $\mathcal{B} (τ\to μ\barν νγ)$. Our predictions also agree with the measurement of $\mathcal{B} (μ\to e \barν νγ)$ by the MEG collaboration. We also report on a recent proposal to test the $τ$ dipole moments via precise measurements of radiative leptonic $τ$ decays at high-luminosity $B$ factories.

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