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We perform a measurement of the tau -> l gamma nu anti-nu (l = e, mu)branching fractions for a minimum photon energy of 10 MeV in the tau restframe, using 431fb^-1 of e^+e^- collisions collected at the center-of-massenergy of the Upsilon(4S) resonance with the BaBar detector at the PEP-IIstorage rings. We find B(tau -> mu gamma nu anti-nu ) =(3.69pm0.03pm0.10)x10^-3, and B(tau -> e gamma nu anti-nu ) =(1.847pm0.015pm0.052)x10^-2, where the first quoted error is statistical, andthe second is systematic. These results are substantially more precise thanprevious measurements.

Measurement of the branching fractions of the radiative leptonic tau decays tau -> e gamma nu anti-nu and tau -> mu gamma nu anti-nu at BaBar