A Search for $B^+ \to \ell^+ \nu_{\ell}$ Recoiling Against $B^{-}\to D^{0} \ell^{-}\bar{\nu} X

We present a search for the decay $\B^+ \to \ell^+ \nu_{\ell} (\ell = \tau, \mu, \mathrm{or} e)$ in $(458.9 \pm 5.1) \times 10^{6}$ $\Upsilon(4S)$ decays recorded with the Babar detector at the SLAC PEP-II $B$-Factory. A sample of events with one reconstructed exclusive semi-leptonic B decay ($B^{-}\to D^{0} \ell^{-}\bar{\nu} X$) is selected, and in the recoil a search for $\B^+ \to \ell^+ \nu_{\ell}$ signal is performed. The $\tau$ is identified in the following channels: $\tau^+ \to e^+ \nu_e \overline{\nu}_\tau$, $\tau^+ \to \mu^+ \nu_{\mu} \overline{\nu}_{\tau}$, $\tau^+ \to \pi^+ \overline{\nu}_{\tau}$, and $\tau^+ \to \pi^+ \pi^{0} \overline{\nu}_{\tau}$. The analysis strategy and the statistical procedure is set up for the branching fraction extraction or upper limit determination. We determine from the dataset a preliminary measurement of $\mathcal{B}(\B^+ \to \tau^+ \nu_{\tau}) = (1.8 \pm 0.8 \pm 0.1) \times 10^{-4}$, which excludes zero at $2.4 \sigma$, and $f_{B} = 230 \pm 57 \mev $. Combination with the hadronically tagged measurement yields $\mathcal{B}(\B^+ \to \tau^+ \nu_{\tau}) = (1.8 \pm 0.6) \times 10^{-4}$. We also set preliminary limits on the branching fractions at $\mathcal{B}(\B^+ \to e^+ \nu_{e}) < 7.7 \times 10^{-6} (\textrm{90% C.L.})$, $\mathcal{B}(\B^+ \to \mu^+ \nu_{\mu}) < 11 \times 10^{-6} (\textrm{90% C.L.})$, and $\mathcal{B}(\B^+ \to \tau^+ \nu_{\tau}) < 3.2 \times 10^{-4} (\textrm{90% C.L.})$.