Search for $B\to \mu {\overline{\nu }}_{\mu }\gamma$ and $B\to e{\overline{\nu }}_e\gamma$

We have searched for the decays $B\to \mu {\overline{\nu }}_{\mu }\gamma$ and $B\to e{\overline{\nu }}_e\gamma$ in a sample of $2.7\times {10}^6$ charged $B$ decays collected with the CLEO II detector. In the muon channel, we observe no candidates in the signal region and set an upper limit on the branching fraction of $\mathcal{B}(B\to \mu {\overline{\nu }}_{\mu }\gamma )<\mathrm{}5.2\mathrm{}\times {10}^{-5}$ at the 90% confidence level. In the electron channel, we observe five candidates in the signal region and set an upper limit on the branching fraction of $\mathcal{B}(B\to e{\overline{\nu }}_e\gamma )<\mathrm{}2.0\mathrm{}\times {10}^{-4}$ at the 90% confidence level.