Search for B+->tau(+)nu

We present a search for the decay B+->tau(+)nu using 383x10(6)B (B) over bar pairs 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 (B--> D(0)l - (v) over bar lX) is selected, and in the recoil a search for B+-> tau(+)nu is performed. The tau is identified in the following channels: tau(+)-> e(+)nu(v) over bar, tau(+)->mu(+)nu(v) over bar, tau(+)->pi(+)(v) over bar, and tau(+)->pi(+)pi(0)(v) over bar. We measure a branching fraction of B(B+->tau(+)nu)=(0.9 +/- 0.6(stat.)+/- 0.1(syst.))x10(-4). In the absence of a significant signal, we calculate an upper limit at the 90% confidence level of B(B+->tau(+)nu)< 1.7x10(-4). We calculate the product of the B meson decay constant f(B) and vertical bar V-ub vertical bar to be f(B)center dot vertical bar V-ub vertical bar=(7.2(-2.8)(+2.0)(stat.)+/- 0.2(syst.))x10(-4) GeV.