Search for lepton-number-violating $B^{\mathbf{+}}\mathbf{\to }{D}^{\mathbf{-}}{\ell }^{\mathbf{+}}{\ell }^{\prime \mathbf{+}}$ decays

We perform the first search for lepton-number-violating $B^{+}\to D^{-}{\ell }^{+}{\ell }^{\prime +}$ decays, where $\ell$ and ${\ell }^{\prime }$ stand for $e$ or $\mu$, using $772\times {10}^6$ $B\overline{B}$ pairs accumulated at the ${\rm Y}(4S)$ resonance with the Belle detector at the KEKB $e^{+}{e}^{-}$ collider. No evidence for these decays has been found. Assuming uniform three-body phase space distributions for the $D^{-}{\ell }^{+}{\ell }^{\prime +}$ decays, we set the following upper limits on the branching fractions at 90% confidence level: $\mathcal{B}(B^{+}\to D^{-}{e}^{+}{e}^{+})<2.6\times {10}^{-6}$, $\mathcal{B}(B^{+}\to D^{-}{e}^{+}{\mu }^{+})<1.8\times {10}^{-6}$ and $\mathcal{B}(B^{+}\to D^{-}{\mu }^{+}{\mu }^{+})<1.1\times {10}^{-6}$.

Figure 1

Feynman diagrams for $B^{+}\to D^{-}{\ell }^{+}{\ell }^{\prime +}$.

Figure 2

The ${\mathcal{R}}_{\mathrm{s}}$ distributions of the signal (solid) and background (dotted for $B\overline{B}$, and dashed for continuum) MC samples for the (a) $D^{-}{e}^{+}{e}^{+}$, (b) $D^{-}{e}^{+}{\mu }^{+}$ and (c) $D^{-}{\mu }^{+}{\mu }^{+}$ modes, respectively.

Figure 3

The 2D fit projections and data for $M_{\mathrm{bc}}$ (left) and $\Delta E$ (right) in the $D^{-}{\mu }^{+}{\mu }^{+}$ mode. In the $M_{\mathrm{bc}}$ ($\Delta E$) projection, $\Delta E$ ($M_{\mathrm{bc}}$) is required to lie in the sideband region. The dotted portion of the fit projection shows the signal region of the displayed variable.

Figure 4

The $M_{\mathrm{bc}}-\Delta E$ distributions for the (a) $D^{-}{e}^{+}{e}^{+}$, (b) $D^{-}{e}^{+}{\mu }^{+}$ and (c) $D^{-}{\mu }^{+}{\mu }^{+}$ final states in data. The boxes indicate the signal regions.