Measurement of the branching fractions of the radiative leptonic $\tau$ decays $\tau \to e\gamma \nu \overline{\nu }$ and $\tau \to \mu \gamma \nu \overline{\nu }$ at BABAR

We perform a measurement of the $\tau \to l\gamma \nu \overline{\nu }$ ($l=e,\mu$) branching fractions for a minimum photon energy of 10 MeV in the $\tau$ rest frame, using $431{\mathrm{fb}}^{-1}$ of $e^{+}{e}^{-}$ collisions collected at the center-of-mass energy of the $\mathrm{\Upsilon }(4S)$ resonance with the BABAR detector at the PEP-II storage rings. We find $\mathcal{B}(\tau \to \mu \gamma \nu \overline{\nu })=(3.69\pm 0.03\pm 0.10)\times 10^{-3}$ and $\mathcal{B}(\tau \to e\gamma \nu \overline{\nu })=(1.847\pm 0.015\pm 0.052)\times 10^{-2}$, where the first quoted error is statistical and the second is systematic. These results are substantially more precise than previous measurements.

Figure 1

Standard Model Feynman diagrams for $\tau \to l\gamma \nu \overline{\nu }$ at tree level.

Figure 2

Selection of the $\tau \to \mu \gamma \nu \overline{\nu }$: (a) distance between lepton and photon candidates on the inner EMC wall, (b) cosine of the angle between momenta of the lepton and photon candidates in the CM frame, (c) invariant mass of the lepton photon pair, and (d) photon candidate energy in the CM frame for radiative $\tau$ decay into a muon after applying all selection criteria except the one on the plotted quantities. The selection criteria on the plotted quantities are highlighted by the vertical lines; we retain the regions indicated by the horizontal arrows.

Figure 3

Selection of the $\tau \to e\gamma \nu \overline{\nu }$ sample: (a) distance between lepton and photon candidates on the inner EMC wall, (b) cosine of the angle between momenta of the lepton and photon candidates in the CM frame, (c) invariant mass of the lepton photon pair, and (d) photon candidate energy in the CM frame for radiative $\tau$ decay into an electron after applying all selection criteria except the one on the plotted quantities. The selection criteria on the plotted quantities are highlighted by the vertical lines; we retain the regions indicated by the horizontal arrows.