  Several extensions of the Standard Model predict the existence of Long-Lived
Neutral Particles (LLNPs) with masses in the multi-GeV range and decay lengths
of O(100 m) or longer. These particles could be copiously produced at the LHC,
but the decay products cannot be detected with the ATLAS or CMS detectors.
MATHUSLA is a proposed large-volume surface detector installed near ATLAS or
CMS aimed to probe scenarios with LLNPs which offers good prospects for
disentangling the physics underlying two-body decays into visible particles. In
this work we focus on LLNP decays into three particles with one of them being
invisible, which are relevant for scenarios with low scale supersymmetry
breaking, feebly interacting dark matter or sterile neutrinos, among others. We
analyze the MATHUSLA prospects to discriminate between two- and three-body LLNP
decays, as well as the prospects for reconstructing the underlying model
parameters.
