  Metastable particles are common in many models of new physics at the TeV
scale. If charged or colored, a reasonable fraction of all such particles
produced at the LHC will stop in the detectors and give observable out of time
decays. We demonstrate that significant information may be learned from such
decays about the properties (e.g. charge or spin) of this particle and of any
other particles to which it decays, for example a dark matter candidate. We
discuss strategies for measuring the type of decay (two- vs three-body), the
types of particles produced, and the angular distribution of the produced
particles using the LHC detectors. We demonstrate that with O(10-100) observed
decay events, not only can the properties of the new particles be measured but
indeed even the Lorentz structure of the decay operator can be distinguished in
the case of three-body decays. These measurements can not only reveal the
correct model of new physics at the TeV scale, but also give information on
physics giving rise to the decay at energy scales far above those the LHC can
probe directly.
