  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 collision 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.
