(a) Diagram of neutrinoless double $\beta$ decay when two neutrons in a nucleus decay simultaneously. (b) The fundamental diagram for changing lepton number by two units.

Feynman diagrams for $B$ decays involving an intermediate heavy neutrino ($N$). (a) $B^-\rightarrow D^{(*)+}\mu^-\mu^-$, (b) $B^-\rightarrow \pi^+(D_s^+)\mu^-\mu^-$, and (c) $B^-\rightarrow D^0 \pi^+\mu^-\mu^-$.

Invariant mass of (a) candidate $J/\psi K^-$ decays, and (b) candidate $J/\psi K^-\pi^+\pi^-$ decays. The data are shown as the points with error bars. Both the partially reconstructed background and the combinatorial background are shown, although the combinatorial background is small and barely visible. The solid curve shows the total. In both cases the candidate $\mu^+\mu^-$ is required to be within $\pm$50 MeV of the $J/\psi$ mass, and in (b) the dimuon pair is constrained to have the $J/\psi$ mass.

Invariant mass spectrum for (a) $B^-\rightarrow D^+\mu^-\mu^-$ candidates, and (b) $B^-\rightarrow D^{*+}\mu^-\mu^-$ candidates. The solid lines show the linear fits to the data in the mass sidebands.

Invariant mass distribution of $\pi^+\mu^-\mu^-$. The estimated backgrounds are also shown. The curve is the sum of the peaking background and the combinatoric background.

Invariant mass distribution of $\pi^+\mu^-$ in the $\pm 2\sigma$ region of the $B^-$ mass with both peaking and combinatorial background superimposed. The peaking background at 3100 MeV is due to misidentified $B^-\rightarrow J/\psi X$ decays.There are two combinations per event.

Majorana mass resolutions for the three $B^-$ decays as a function of Majorana mass.

Detection efficiencies for the three $B^-$ decays as a function of Majorana mass. Charm meson decay branching fractions are not included.

Upper limits at 95% CL as a function of the putative Majorana neutrino mass, (a) for ${\cal{B}}(B^- \rightarrow \pi^+\mu^- \mu^-)$ as a function of the $\pi^+\mu^-$ mass, (b) for ${\cal{B}}(B^-\rightarrow D_s^+\mu^-\mu^-$) as a function of the $D_s^+\mu^-$ mass, and (c) for ${\cal{B}}(B^-\rightarrow D^0\pi^+\mu^-\mu^-)$ as a function of the $\pi^+\mu^-$ mass.

Invariant mass spectrum for $B^-\rightarrow D_s^+\mu^-\mu^-$ candidates. The line shows the fit to the data excluding the $B^-$ mass signal region.

Invariant mass spectrum of $D_s^+\mu^-$ from $B^-\rightarrow D_s^+\mu^-\mu^-$ events in the signal region with the background estimate superimposed (solid curve). There are two combinations per event.

Invariant mass distribution of $D^0\pi^+ \mu^- \mu^- $. The solid line shows a linear fit to the data in the sidebands of the $B^-$ signal region.

Invariant mass distribution of $\pi^+\mu^-$ for $B^-\rightarrow D^0\mu^-\mu^- \pi^+$ in the signal region and with estimated background distribution superimposed. There are two combinations per event.

Relative efficiencies as a function of Majorana neutrino lifetime for (a) $B^-\rightarrow \pi^+\mu^-\mu^-$ for a mass of 3 GeV, (b) $B^-\rightarrow D_s^+\mu^-\mu^-$ for a mass of 3 GeV, and (c) $B^-\rightarrow D^0\pi^+\mu^-\mu^-$ for a Majorana neutrino mass of 2 GeV. Where the error bars are not visible, they are smaller than radii of the points.

Upper limits on $|V_{\mu4}|^2$ at 95% CL as a function of the Majorana neutrino mass from the $B^- \rightarrow \pi^+ \mu^- \mu^-$ channel.

Animated gif made out of all figures.

Charm and charmonium branching fractions

Systematic uncertainties for $B^- \rightarrow D X \mu^- \mu^-$ modes.

Systematic uncertainties for $B^- \rightarrow \pi^+\mu^- \mu^- $ measurement.

Summary of upper limits on branching fractions. Both the limits on the overall branching fraction assuming a phase space decay, and the range of limits on the branching fraction as a function of Majorana neutrino mass ($M_N$) are given. All limits are at 95% CL.