Search for the Decay ${\mathit{B}}^0\to \gamma \gamma$

We present a limit on the branching fraction for the decay $B^0\to \gamma \gamma$ using data collected at the $\Upsilon \left(4S\right)$ resonance with the BABAR detector at the PEP-II asymmetric energy $e^{+}{e}^{-}$ collider. Based on the observation of one event in the signal region, out of a sample of $21.3\times {10}^6$ $e^{+}{e}^{-}\to \Upsilon \left(4S\right)\to B\overline{B}$ decays, we establish an upper limit on the branching fraction of $B(B^0\to \gamma \gamma )<1.7\mathrm{}\times {10}^{-6\mathrm{}}$ at the $90\%$ confidence level. This result substantially improves upon existing limits.