Mass shell technique for measuring masses of a pair of semi-invisibly decaying particles

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 measurable 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 efficiently. These are compared with a selection of variables in the literature, and possible applications at lepton and hadron colliders are discussed.