Sterile neutrinos in ${\Lambda }_b^0\to ({\Lambda }_c^{+},p^{+}){\ell }_1^{-}{\ell }_2^{-}{\ell }_3^{+}\nu$ decays

Abstract

We study lepton number violating and lepton number conserving semi-leptonic decays of heavy baryons ${\Lambda }_b^0$ 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 $|V_{\mu N}|$, CP-averaged branching ratio of ${\Lambda }_b^0\to ({\Lambda }_c,p)\mu \mu e\nu$ with intermediate Majorana neutrinos is almost two orders of magnitude larger than for the same with Dirac neutrinos, whereas, CP-averaged branching ratio of ${\Lambda }_b^0\to ({\Lambda }_c,p)ee\mu \nu$ 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.