Three-step cascade decays into two invisible particles and two visible particles via two intermediate on-shell particles develop cusped peak structures in several kinematic distributions. We study the basic properties of the cusps and endpoints in va
rious distributions and demonstrate that the masses of the missing particles and the intermediate particles can be determined by the cusp and endpoint positions. Effects from realistic considerations such as finite decay widths, longitudinal boost of the parent particle, and spin correlations are shown to be under control for the processes illustrated.
The kinematics of a final state system with two invisible particles and two visible particles can develop cusped peak structures. This happens when the system has a fixed invariant mass (such as from a narrow resonant particle decay or with a fixed c
ollision c.m. energy) and undergoes decays of two on-shell intermediate particles. Focusing on the antler decay topology, we derive general analytic expressions for the invariant mass distribution and the kinematic cusp position. The sharp cusp peaks and the endpoint positions can help to determine the masses of the missing particles and the intermediate particles. We also consider transverse momentum variables and angular variables. In various distributions the kinematic cusp peaks are present and pronounced. We also study the effects on such kinematic cusp structures from realistic considerations including finite decay widths, the longitudinal boost of the system, and spin correlations.
