On the collider-testability of the type-I seesaw model with 3 right-handed neutrinos

If any heavy neutral leptons are discovered in accelerator-based experiments, key questions will involve their possible connection to neutrino masses or leptogenesis. Working in a renormalisable extension of the Standard Model by three right-handed neutrinos, we address the question of how much information about the fundamental model parameters can be obtained by measuring the branching ratios in the decays of the heavy neutral leptons into individual SM generations. We find that, provided that these branching ratios could be measured with arbitrary precision and assuming kinematically distinguishable right-handed neutrinos, they can be sufficient to pin down all 18 parameters of the model when supplemented with light neutrino oscillation data. When considering a finite statistical uncertainty comparable to that which can be achieved by future lepton colliders like FCC-ee or CEPC in the mass range of tens of GeV, some parameter degeneracies remain, but measurements would still provide powerful consistency checks of the model. In the sub-GeV range a good sensitivity to individual model parameters can be expected for SHiP and potentially for DUNE. This shows the potential of these experiments to not only discover heavy neutral leptons, but play an important role in understanding their role in particle physics and cosmology.