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We search for the rare leptonic decay B+ --> tau+ nu_tau in a sample of
232x10^6 BBbar pairs collected with the BABAR detector at the SLAC
PEP-II B-Factory. Signal events are selected by examining the properties
of the B meson recoiling against the semileptonic decay
B- --> D*0 l- nu_lbar. We find no evidence for a signal and set an
upper limit on the branching fraction of
BR(B+ --> tau+ nu_tau) < 2.8x10^{-4} at the 90% confidence level.
We combine this result with a previous, statistically
independent BABAR search for B+ --> tau+ nu_tau to give an upper limit of
BR(B+ --> tau+ nu_tau) < 2.6x10^{-4} at the 90% confidence level.
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