A Search for B+ --> tau+ nu Recoiling Against B- --> D0 l- nubar X

We present a search for the decay $B^{+} \to \tau^{+} \nu_{\tau}$ using 288 fb-1 of data collected at the $\Upsilon(4S)$ resonance with the BaBar detector at the SLAC PEP-II $B$-Factory. A sample of events with one reconstructed semileptonic B decay is selected, and in the recoil a search for $B^{+} \to \tau^{+} \nu_{\tau}$ signal is performed. The $\tau$ is identified in the following channels: {\tau^+ \to e^+ \nu_e \nutb}, {\tau^+ \to \mu^+ \nu_{\mu} \nutb}, {\tau^+ \to \pi^+ \nutb} and {\tau^+ \to \pi^+ \pi^0 \nutb}. We measure a branching fraction of $\mathcal{B}(B^{+} \to \tau^{+} \nu_{\tau})=(0.88^{+0.68}_{-0.67}({stat.}) \pm 0.11 ({syst.})) \times 10^{-4}$ and extract an upper limit on the branching fraction, at the 90% confidence level, of $\mathcal{B}(B^{+} \to \tau^{+} \nu_{\tau}) < 1.8 \times 10^{-4}$. We calculate the product of the $B$ meson decay constant and $|\Vub|$ to be $f_{B}\cdot|\Vub| = (7.0^{+2.3}_{-3.6}({stat.})^{+0.4}_{-0.5}({syst.}))\times10^{-4}$ GeV \.