  Motivated by evidence for the existence of dark matter, many new physics
models predict the pair production of new particles, followed by the decays
into two invisible particles, leading to a momentum imbalance in the visible
system. For the cases where all four components of the vector sum of the two
`missing' momenta are measured from the momentum imbalance, we present analytic
solutions of the final state system in terms of measureable momenta, with the
mass shell constraints taken into account. We then introduce new variables
which allow the masses involved in the new physics process, including that of
the dark matter particles, to be extracted. These are compared with a selection
of variables in the literature, and possible applications at lepton and hadron
colliders are discussed.
