  We consider the decay of a generic resonance to two visible particles and any
number of invisible particles. We show that the shape of the invariant mass
distribution of the two visible particles is sensitive to both the mass
spectrum of the new particles, as well as the decay topology. We provide the
analytical formulas describing the invariant mass shapes for the nine simplest
topologies (with up to two invisible particles in the final state). Any such
distribution can be simply categorized by its endpoint, peak location and
curvature, which are typically sufficient to discriminate among the competing
topologies. In each case, we list the effective mass parameters which can be
measured by experiment. In certain cases, the invariant mass shape is
sufficient to completely determine the new particle mass spectrum, including
the overall mass scale.
