Abstract
We present a search for the decay B+ -->tau+ nu using 467.8 x 10^6 B B pairs collected at the Y(4S) resonance with the BaBar detector at the SLAC PEP-II B-Factory. We select a sample of events with one completely reconstructed B- in the hadronic decay modes (B- --> D(*)0 X- and B- --> J/\psi X-). We examine the rest of the event to search for a B+ --> tau+ nu decay. We identify the tau+ lepton in the following modes: tau+ --> e+ nu nu, tau+ --> mu+ nu nu, tau+ --> pi+ nu, and tau+ --> rho+ nu. We find an excess of events with respect to the expected background, which excludes the null signal hypothesis at the level of 3.8 sigma (including systematic uncertainties) and corresponds to a branching fraction central value of B(B+ --> tau+ nu)=(1.83^{+0.53}_{-0.49}(stat.) +/- 0.24 (syst.)) x 10^-4.