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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.
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