Measurement of the branching fractions of the radiative leptonic $τ$ decays $τ \to eγν¯ν$ and $τ \to µγν¯ν$ at $B\small AB\small AR$

We perform a measurement of the τ→lγνν¯ (l=e,μ) branching fractions for a minimum photon energy of 10 MeV in the τ rest frame, using 431fb-1 of e+e- collisions collected at the center-of-mass energy of the (4S) resonance with the BABAR detector at the PEP-II storage rings. We find B(τ→μγνν¯)=(3.69±0.03±0.10)×10-3 and B(τ→eγνν¯)=(1.847±0.015±0.052)×10-2, where the first quoted error is statistical and the second is systematic. These results are substantially more precise than previous measurements.