Searching for lepton number violating $\Lambda$ baryon decays mediated by GeV-scale Majorana neutrino with LHCb

Abstract

We consider the lepton-number-violating processes in $\Lambda_b$/$\Lambda_c$ decays mediated by on-shell GeV-scale sterile neutrino. We calculate the branching ratio for the following processes: $\Lambda_b^{0} \rightarrow \mathcal{B}^+ \mu^{-}\mu^- \pi^+$, where $\mathcal{B}^+$ is $\Lambda_c^+$ or proton, and $\Lambda_c^{+} \rightarrow \Lambda \mu^{+}\mu^+ \pi^-$, as function of the mass of the sterile neutrino $m_N$ and the heavy-light mixing coefficient of the extended Pontecorvo-Maki-Nakagawa-Sakata (PMNS) matrix $|U_{\mu N}|^2$. The effect of finite detector size is included in our calculation. After comparing the theoretical effective branching ratio with the expected experimental ability of LHCb, we give the sensitivity upper bounds on $|U_{\mu N}|^2$ on the ($|U_{\mu N}|^2$-$m_N$) plane. These channels give comparable results with the bounds given by different search strategies (e.g., at Belle, NuTeV, DELPHI and BEBC) in the mass region $m_N \simeq$ 0.25 GeV - 4.5 GeV, and the limits are stronger in the mass range 2 GeV $<m_N<$ 4.5 GeV.