Lepton number violating and conserving heavy baryon four-body decays in the presence of two almost degenerate heavy neutrinos
We study the four-body heavy baryon decay, including two leptons in the final state, of the form $B_A \to B_B P \ell_α\ell_β$, which can be either a lepton number conserving (LNC) or a lepton number violating (LNV) process (where $B$, $P$ and $\ell$ are baryons, pseudoscalar mesons and leptons, respectively), including all kinematic allowed lepton pair possibilities. We work beyond the simplified assumption of a single heavy Majorana neutrino mixing with the active sector, considering potential interference effects when including two nearly degenerate heavy Majorana neutrinos. Particularly, we provide a first estimate of the decay channels involving different flavors for the external leptons (e.g., muon-tau), and elaborate on the interference pattern due to leptons exchange. We show that the results for the two heavy almost degenerate neutrinos can be recast into a single Majorana neutrino, and exhibit the features for both the LNC and LNV scenarios. We determine the potential exclusion region for the mass and heavy-light mixing parameters, of the neutrinos driving the decay, including finite size detector effects, and compare them with those from direct searches and $τ$ and meson decays. We also obtain the Branching ratio as a function of the heavy neutrino mass for the current upper limit of the heavy-light mixings.