Sensitivity to Majorana neutrinos in $\mathrm{\Delta }L=2$ decays of $B_c$ meson at LHCb

The possible existence of Majorana neutrinos can be tested through the study of processes where the total lepton number $L$ is violated by two units ($\mathrm{\Delta }L=2$). In this work, the production of an on-shell Majorana neutrino with a mass around $\sim 0.2\mathrm{GeV}$ to a few GeV is studied in $\mathrm{\Delta }L=2$ decays of the $B_c$ meson. We focus on the same-sign di-muon channels: three-body $B_c^{-}\to {\pi }^{+}{\mu }^{-}{\mu }^{-}$ and four-body $B_c^{-}\to J/\psi {\pi }^{+}{\mu }^{-}{\mu }^{-}$ and their experimental sensitivity at the LHCb. In both channels, we find that sensitivities on the branching fraction of the order $\lesssim {10}^{-7}({10}^{-8})$ might be accessible at the LHC run 2 (future LHC run 3), allowing us to set additional and complementary constraints on the parameter space associated with the mass and mixings of the Majorana neutrino. In particular, bounds can be obtained on the mixing $|V_{\mu N}{|}^2\sim \mathcal{O}({10}^{-5}–{10}^{-4})$ that are similar or better that the ones obtained from heavy meson $\mathrm{\Delta }L=2$ decays: $D_{(s)}^{-}\to {\pi }^{+}{\mu }^{-}{\mu }^{-}$ and $B^{-}\to {\pi }^{+}{\mu }^{-}{\mu }^{-}(D^0{\pi }^{+}{\mu }^{-}{\mu }^{-})$.

Figure 1

Current experimental upper limits (UL) on branching ratios of three- (top) and four-body (bottom) $\mathrm{\Delta }L=2$ decays [23]. Taken from PDG [1] and BABAR [25, 26], LHCb [27, 28, 29], Belle [30, 31], and E791 [32] Collaborations. For simplicity, we have not included the UL on $B^{-}\to V^{+}{\ell }^{-}{\ell }^{\prime -}$, with $V=\rho ,K^{*},D^{*}$, which are typically of the order $\lesssim {10}^{-7}$ [26].

Figure 2

$\mathrm{\Delta }L=2$ decays of $B_c$ meson mediated by a Majorana neutrino $N$: (a) three-body $B_c^{-}\to {\pi }^{+}{\mu }^{-}{\mu }^{-}$ and (b) four-body $B_c^{-}\to J/\psi {\pi }^{+}{\mu }^{-}{\mu }^{-}$ channels.

Figure 3

Number of expected events of the $\mathrm{\Delta }L=2$ process $B_c^{-}\to {\pi }^{+}{\mu }^{-}{\mu }^{-}$ and $B_c^{-}\to J/\psi {\pi }^{+}{\mu }^{-}{\mu }^{-}$ to be observed in the LHCb experiment as a function of the branching ratio, for the different integrated luminosity collected: Blue LHC run 1 ($3{\mathrm{fb}}^{-1}$), red LHC run 2 ($5{\mathrm{fb}}^{-1}$), and purple LHC run 3 ($40{\mathrm{fb}}^{-1}$). Filled area shows the uncertainty in the computation.

Figure 4

Exclusion regions on $(m_N,|V_{\mu N}{|}^2)$ plane, from LNV di-muon modes. The black (blue) region represents the constraint obtained from the search on $B_c^{-}\to {\pi }^{+}{\mu }^{-}{\mu }^{-}$ at LHCb for LHC run 2 (LHC run 3). Updated constraints provided by $(K^{-},D_{(s)}^{-},B^{-})\to {\pi }^{+}{\mu }^{-}{\mu }^{-}$ and $B^{-}\to D^0{\pi }^{+}{\mu }^{-}{\mu }^{-}$ are also included for comparison.

Figure 5

Same description as in Fig. 4, but the black (blue) region represents the constraint obtained from the search on $B_c^{-}\to J/\psi {\pi }^{+}{\mu }^{-}{\mu }^{-}$ at LHCb for LHC run 2 (LHC run 3).