| Abstract |
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% $Id: abstract.tex,v 1.4 2007/04/14 16:43:30 edward Exp $
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We present the results of a search for $B^{+}\rightarrow\gamma \ell^{+}\nu_{\ell}$,
where $\ell = e, \mu$.
We use a sample of 232 million $B\bar{B}$ pairs recorded at the $\Upsilon(4S)$
with the BaBar detector at the PEP-II $B$~Factory.
We measure a partial branching fraction $\Delta\mathcal{B}$ in a restricted region
of phase space that reduces the effect of theoretical uncertainties,
requiring the lepton energy to be between $1.875$ and $2.850$GeV,
the photon energy to be between $0.45$ and $2.35$GeV, and
the cosine of the angle between the lepton and photon momenta to
be less than $-0.36$, with all quantities computed in the $\Upsilon(4S)$
center-of-mass frame. We find
$\Delta\mathcal{B}(B^{+}\rightarrow\gamma \ell^{+}\nu_{\ell}) =
(-0.3^{+1.3}_{-1.5}(\mbox{stat})\pm0.6(\mbox{syst})\pm0.1(\mbox{th}))\times10^{-6}$,
assuming lepton universality.
Interpreted as a 90\% C.L.
Bayesian upper limit, the result corresponds to $1.7\times10^{-6}$
for a prior flat in amplitude, and $2.3\times10^{-6}$
for a prior flat in branching fraction.
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