Search for the radiative leptonic decay $B \rightarrow \gamma \ell\bar{\nu_{\ell}}$

We present the results of a search for charged $B$ meson decays into $\gamma \ell \bar{\nu_{\ell}}$, where $\ell = e, \mu$. We use a sample of approximately 232 million $B\bar{B}$ pairs recorded at the $\Upsilon(4S)$ resonance by the BaBar detector at the PEP-II asymmetric-energy $B$~Factory at SLAC. This decay mode is related to the theoretically clean purely leptonic decay, but with a larger branching fraction due to the lack of helicity supression. An observation of this decay could be used either to evaluate the $B$ meson pseudoscalar decay constant $f_B$ or, with an independent determination of $f_B$, to test theoretical models of charmless $B$ decays.