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

Abstract

Lepton-number violation can be induced by the exchange of an on-shell Majorana neutrino $N$ in semileptonic $|\Delta L|=2$ 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] ps and integrated luminosities collected of 10 and 50 fb${}^{-1}$ at the LHCb and 30, 300, and 3000 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 $m_N\in [0.25,4.77]$ GeV and $m_N\in [0.25,3.29]$ 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).

Comments: 11 pages, 6 figures. V3: discussion in Sec. IV improved, matches with version published in Phys. Rev. D. arXiv admin note: substantial text overlap with arXiv:1705.10606, arXiv:1604.03177