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Sterile neutrinos in $Λ_b^0\to (Λ_c^+,p^+)\ell^-_1\ell^-_2\ell^+_3ν$ decays

We study lepton number violating and lepton number conserving semi-leptonic decays of heavy baryons $Λ_b^0$ to three charged leptons and a neutrino. The decays occur through two intermediate quasi-degenerate GeV-scale sterile neutrinos of either Majorana or Dirac type that can be on-shell. Interference between the intermediate heavy neutrinos leads to CP violation in the final states. Effect of neutrino oscillations between the heavy states are also considered in observables of interests, \emph{i.e.,} branching ratio, and the CP-asymmetry. Given the present constraints on the heavy-to-light mixing elements $|V_{eN}|$ and $|V_{μN}|$, CP-averaged branching ratio of $Λ_b^0\to (Λ_c,p)μμeν$ with intermediate Majorana neutrinos is almost two orders of magnitude larger than for the same with Dirac neutrinos, whereas, CP-averaged branching ratio of $Λ_b^0\to (Λ_c,p)eeμν$ is of the same order of magnitude for both Majorana and Dirac neutrino induced decays. CP-violation is found to be appreciable when the neutrino mass difference is comparable with the average decay widths.