  We show that mass measurements for new particles appearing in decay chains
can be improved by determining the boundary of the available phase space in its
full dimensionality rather than by using one-dimensional kinematic features for
each stage of the cascade decay. This is demonstrated for the case of one
particle decaying to three visible and one invisible particles in a two-stage
cascade, but our methods also apply to a more general set of decay topologies.
We show that not only mass differences, but also the overall scale of masses
can be determined with high precision without having to rely on cross section
information. The improvement arises from the properties of the higher
dimensional phase space itself, independent of the matrix element for the
decay, and it is not weakened by the presence of intermediate on-shell
particles in the cascade. Our results are particularly significant for the case
of low signal statistics, a distinct possibility for new physics searches in
the near future.
