  We consider the application of endpoint techniques to the problem of mass
determination for new particles produced at a hadron collider, where these
particles decay to an invisible particle of unknown mass and one or more
visible particles of known mass. We also consider decays of these types for
pair-produced particles and in each case consider situations both with and
without initial state radiation. We prove that, in most (but not all) cases,
the endpoint of an appropriate transverse mass observable, considered as a
function of the unknown mass of the invisible particle, has a kink at the true
value of the invisible particle mass. The co-ordinates of the kink yield the
masses of the decaying particle and the invisible particle. We discuss the
prospects for implementing this method at the LHC.
