CP violation with GeV-scale Majorana neutrino in $\Lambda_b\to(\Lambda_c^+, p^+)\pi^+\mu^-\mu^-$ decays

We explore the possibility of CP violation in baryonic $\Lambda_b\to(\Lambda_c^+, p^+)\pi^+\mu^-\mu^-$ decays which are mediated by two Majorana sterile neutrino and are $|\Delta L|=2$ lepton number violating processes. Appreciable CP asymmetry can be obtained if there are two on-shell Majorana neutrinos that are quasi-degenerate in mass with the mass difference of the order of average decay widths. We find that given the present constraints on the heavy to light mixing element $|V_{\mu N}|$, the $\Lambda_b\to p^+\pi^+\mu^-\mu^-$ and $\Lambda_b\to \Lambda_c^+\pi^+\mu^-\mu^-$ decay rates are suppressed but could be within the experimental reach at the LHC. If searches of the modes are performed, then experimental limits on the rates can be translated to constraints on the Majorana neutrino mass $m_N$ and heavy to light mixing element squared $|V_{\mu N}|^2$. We show that the constraints on the $(m_N, |V_{\mu N}|^2)$ parameter space coming from the $|\Delta L| = 2$ baryonic decays are complementary to the bounds coming from other processes.