Scalar three-body decays and signals for new physics

If massive invisible particles are pair-produced in a three-body decay, then the energy distribution of the other (visible) product is sensitive to the mass of the invisible pair. We use this fact in the context of a Higgs boson decaying into (i)a Z-boson and two massive neutrinos of a fourth generation, and (ii)a Z and two lightest particles in the minimal supersymmetric standard model. We discuss how the Z-energy spectrum in each case can reflect the values of the parameters in such models. (3 figures, hard copies available from authers on request).