Probing the Nature of Heavy Neutral Leptons in Direct Searches and Neutrinoless Double Beta Decay

Heavy Neutral Leptons (HNLs) are a popular extension of the Standard Model to explain the lightness of neutrino masses and the matter-antimatter asymmetry through leptogenesis. Future direct searches, such as fixed target setups like DUNE, and neutrinoless double beta decay are both expected to probe the regime of active-sterile neutrino mixing in a standard Seesaw scenario of neutrino mass generation for HNL masses around m_N <~ 1 GeV. Motivated by this, we analyse the complementarity between future direct searches and neutrinoless double beta decay to probe the nature of HNLs, i.e., whether they are Majorana or quasi-Dirac states, and CP-violating phases in the sterile neutrino sector. Following an analytic discussion of the complementarity, we implement a generic fixed target experiment modelling DUNE. We perform a statistical study in how a combined search for HNLs in direct searches and neutrinoless double beta decay, using DUNE and LEGEND-1000 as representative examples, can probe the nature of sterile neutrinos.