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Neutrinoless double beta decay versus other probes of heavy sterile neutrinos

We make a comparative study of the neutrinoless double beta decay constraints on heavy sterile neutrinos versus other direct and indirect constraints from both lepton number conserving and violating processes, as a sensitive probe of the extent of lepton number violation and possible interference effects in the sterile sector. We introduce a phenomenological parametrisation of the simplified one-generation seesaw model with one active and two sterile neutrino states in terms of experimentally measurable quantities, such as active-sterile neutrino mixing angles, CP phases, masses and mass splittings. This simple parametrisation enables us to analytically derive a spectrum of possible scenarios between the canonical seesaw with purely Majorana heavy neutrinos and inverse seesaw with pseudo-Dirac ones. We then go on to constrain the simplified parameters of this model from various experiments at the energy, intensity and cosmic frontiers. We emphasise that the constraints from lepton number violating processes strongly depend on the mass splitting between the two sterile states and the relative CP phase between them. This is particularly relevant for neutrinoless double beta decay, which is weakened for small mass splitting and opposite CP parities between the sterile states. On the other hand, neutrinoless double beta decay is especially sensitive for Majorana sterile neutrinos with masses around $0.1-10$ GeV.