Search for $B^0$ decays to invisible final states ($+\gamma$) at Belle

We report searches for $B^0\to \text{invisible}$ and $B^0\to \text{invisible}+\gamma$ decays, where the energy of the photon is required to be larger than 0.5 GeV. These results are obtained from a $711{\mathrm{fb}}^{-1}$ data sample that contains $772\times {10}^{6}B\overline{B}$ pairs and was collected near the $\mathrm{\Upsilon }(4S)$ 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% confidence level of $\mathcal{B}(B^0\to \text{invisible})<7.8\times {10}^{-5}$ and $\mathcal{B}(B^0\to \text{invisible}+\gamma )<1.6\times {10}^{-5}$.

Figure 1

Feynman diagrams for $B^0\to (\gamma )\nu \overline{\nu }$ in the Standard Model.

Figure 2

$O_{\mathrm{tag}}$ (left) and $O_{\text{shape}}$ (right) distributions for continuum (blue and hatched area), generic $B$ (green and shaded area) background, and signal MC simulation (red and blank area). Top, $B^0\to \text{invisible}$; bottom, $B^0\to \text{invisible}+\gamma$. Histograms are normalized such that the sum of all bins equals one.

Figure 3

Left, Comparison of $E_{\mathrm{ECL}}$ distributions between background MC simulation and data in the $O_{\mathrm{tag}}$ sideband. The black points are data. The blue crosses with a shaded error band are the background MC simulation. Right, Comparison of $E_{\mathrm{ECL}}$ distributions between $B^0\to \nu \overline{\nu }$ signal MC simulation and $B^0\to D^{*-}{l}^{+}\nu$ data. The black points are data. The red and shaded distribution is signal MC simulation. Histograms are normalized such that the sum of all bins equals one.

Figure 4

Verification of the background ratio in MC simulation in the $O_{\mathrm{tag}}$ sideband. Dots with error bars are data, black solid line is the fit result, green short-dashed line is the generic $B$ background component and blue dash-dotted line is the non-$B$ background component.

Figure 5

Projections of the fit result on $\cos {\theta }_T$ (left) and $E_{\mathrm{ECL}}$ (right) for $B^0\to \text{invisible}$. Dots with error bars are data, black solid line is the fit result, red dotted line is the signal component, green short-dashed line is the generic $B$ background component and blue dash-dotted line is the non-$B$ background component.

Figure 6

Fitting result of the control sample $B^0\to D^{-}{l}^{+}\nu$ in the $E_{\mathrm{ECL}}$ signal box (left) and sideband (right). Selections are based on $B^0\to \text{invisible}+\gamma$. Dots with error bars are data, black solid line is the combined fit result, red dashed line is the signal component and blue dash-dotted line is background.

Figure 7

$M_{\mathrm{miss}}^2$ (left) and $E_{\mathrm{ECL}}$ (right) distributions of data and the expected background for $B^0\to \text{invisible}+\gamma$. The $M_{\mathrm{miss}}^2$ distribution is plotted in the $E_{\mathrm{ECL}}$ signal box and the $E_{\mathrm{ECL}}$ distribution is plotted in the whole $M_{\mathrm{miss}}^2$ region. The black points with error are data. The gray crosses with a shaded error band are the expected background.