  SHiP is a proposed high-intensity beam dump experiment set to operate at the
CERN SPS. It is expected to have an unprecedented sensitivity to a variety of
models containing feebly interacting particles, such as Heavy Neutral Leptons
(HNLs). Two HNLs or more could successfully explain the observed neutrino
masses through the seesaw mechanism. If, in addition, they are
quasi-degenerate, they could be responsible for the baryon asymmetry of the
Universe. Depending on their mass splitting, HNLs can have very different
phenomenologies: they can behave as Majorana fermions -- with lepton number
violating (LNV) signatures, such as same-sign dilepton decays -- or as Dirac
fermions with only lepton number conserving (LNC) signatures. In this work, we
quantitatively demonstrate that LNV processes can be distinguished from LNC
ones at SHiP, using only the angular distribution of the HNL decay products.
Accounting for spin correlations in the simulation and using boosted decision
trees for discrimination, we show that SHiP will be able to distinguish
Majorana-like and Dirac-like HNLs in a significant fraction of the currently
unconstrained parameter space. If the mass splitting is of order $10^{-6}$ eV,
SHiP could even be capable of resolving HNL oscillations, thus providing a
direct measurement of the mass splitting. This analysis highlights the
potential of SHiP to not only search for feebly interacting particles, but also
perform model selection.
