Lepton-number violation in $B_s$ meson decays induced by an on-shell Majorana neutrino

Lepton-number violation can be induced by the exchange of an on-shell Majorana neutrino $N$ in semileptonic $|\mathrm{\Delta }L|=2$ decays of the $B_s$ meson, $B_s^0\to P^{-}{\pi }^{-}{\mu }^{+}{\mu }^{+}$ with $P=K,D_s$. We investigate the production of such a heavy sterile neutrino through these four-body ${\mu }^{+}{\mu }^{+}$ channels and explore the sensitivity that can be reached at the LHCb and CMS experiments. For heavy neutrino lifetimes of ${\tau }_N=[1,100,1000]\mathrm{ps}$ and integrated luminosities collected of 10 and $50{\mathrm{fb}}^{-1}$ at the LHCb and 30, 300, and $3000{\mathrm{fb}}^{-1}$ at the CMS, we find a significant sensitivity on branching fractions of the orders $\mathrm{BR}(B_s^0\to K^{-}{\pi }^{-}{\mu }^{+}{\mu }^{+})\lesssim \mathcal{O}({10}^{-9}–{10}^{-8})$ and $\mathrm{BR}(B_s^0\to D_s^{-}{\pi }^{-}{\mu }^{+}{\mu }^{+})\lesssim \mathcal{O}({10}^{-8}–{10}^{-7})$. In the kinematically allowed mass ranges of $m_N\in [0.25,4.77]\mathrm{GeV}$ and $m_N\in [0.25,3.29]\mathrm{GeV}$, respectively, we exclude regions on the parameter space $(m_N,|V_{\mu N}{|}^2)$ associated with the heavy neutrino, which could slightly improve the limits from $B^{-}\to {\pi }^{+}{\mu }^{-}{\mu }^{-}$ (LHCb).

Figure 1

Number of expected events of the process $B_s^0\to K^{-}{\pi }^{-}{\mu }^{+}{\mu }^{+}$ (top) and $B_s^0\to D_s^{-}{\pi }^{-}{\mu }^{+}{\mu }^{+}$ (bottom) to be observed in the LHCb experiment as a function of their branching fractions for a luminosity of $10{\mathrm{fb}}^{-1}$ (red) and $50{\mathrm{fb}}^{-1}$ (magenta). The solid black line shows the central value, while the filled area shows the $1\text{−}\sigma$ uncertainty.

Figure 2

Expected events in the CMS experiment for $B_s^0\to K^{-}{\pi }^{-}{\mu }^{+}{\mu }^{+}$ (top) and $B_s^0\to D_s^{-}{\pi }^{-}{\mu }^{+}{\mu }^{+}$ (bottom) as a function of the branching fraction of the final state considered and for three benchmark luminosities: 30 (green), 300 (blue), and 3000 (gray) ${\mathrm{fb}}^{-1}$. The central value is shown with a solid line. The shaded area represents the associated uncertainty in a $1\text{−}\sigma$ window.

Figure 3

Heavy neutrino lifetime ${\tau }_N$ as a function of $m_N$. The blue and red bands correspond to the allowed parameter spaces for $|V_{\tau N}{|}^2={10}^{-3}$ and ${10}^{-2}$, respectively, while $|V_{eN}{|}^2$ and $|V_{\mu N}{|}^2$ vary within the range $[{10}^{-7},{10}^{-3}]$.

Figure 4

Exclusion regions on the $(m_N,|V_{\mu N}{|}^2)$ plane for (a) $\mathrm{BR}(B_s^0\to K^{-}{\pi }^{-}{\mu }^{+}{\mu }^{+})<{10}^{-8}$ and (b) $\mathrm{BR}(B_s^0\to K^{-}{\pi }^{-}{\mu }^{+}{\mu }^{+})<{10}^{-9}$. The black, blue, and gray regions represent the bounds obtained for heavy neutrino lifetimes of ${\tau }_N=1$, 100, 1000 ps, respectively. Limits provided by $K^{-}\to {\pi }^{+}{\mu }^{-}{\mu }^{-}$ [38] and $B^{-}\to {\pi }^{+}{\mu }^{-}{\mu }^{-}$ [32] are also included for comparison.

Figure 5

The same caption as in Fig. 4 but for (a) $\mathrm{BR}(B_s^0\to D_s^{-}{\pi }^{-}{\mu }^{+}{\mu }^{+})<{10}^{-7}$ and (b) $\mathrm{BR}(B_s^0\to D_s^{-}{\pi }^{-}{\mu }^{+}{\mu }^{+})<{10}^{-8}$.

Figure 6

Exclusion regions on the $(m_N,|V_{\mu N}{|}^2)$ plane coming from the Belle [67], DELPHI [68], NA3 [69], CHARMII [70], and NuTeV [71] experiments. Limits provided by the searches on $B_s^0\to (K^{-},D_s^{-}){\pi }^{-}{\mu }^{+}{\mu }^{+}$ are represented by the gray and black regions, respectively. See the text for details.