Search for $B^0$ Decays to Invisible Final States ($+\gamma$) at Belle

We report searches for $B^0\to \mathrm{i}\mathrm{n}\mathrm{v}\mathrm{i}\mathrm{s}\mathrm{i}\mathrm{b}\mathrm{l}\mathrm{e}$ and $B^0\to \mathrm{i}\mathrm{n}\mathrm{v}\mathrm{i}\mathrm{s}\mathrm{i}\mathrm{b}\mathrm{l}\mathrm{e}+\gamma$ decays, where the energy of the photon is required to be larger than 0.5 GeV. These results are obtained from a $711{\mathrm{f}\mathrm{b}}^{-1}$ data sample that contains $772\times {10}^{6}B\bar{B}$ pairs and was collected near the $\mathrm{{\rm Y}}(4S)$ resonance with the Belle detector at the KEKB $e^{+}{e}^{-}$ collider. We observe no significant signal for either decay and set upper limits on their branching fractions at $90\mathrm{\%}$ confidence level of $\mathcal{B}(B^0\to \mathrm{i}\mathrm{n}\mathrm{v}\mathrm{i}\mathrm{s}\mathrm{i}\mathrm{b}\mathrm{l}\mathrm{e})<7.8\times {10}^{-5}$ and $\mathcal{B}(B^0\to \mathrm{i}\mathrm{n}\mathrm{v}\mathrm{i}\mathrm{s}\mathrm{i}\mathrm{b}\mathrm{l}\mathrm{e}+\gamma )<1.6\times {10}^{-5}$.