  We study theoretical and experimental facets of mass determination of new
particle states. Assuming supersymmetry, we update the quark and lepton mass
matrices at the grand unification scale accounting for threshold corrections
enhanced by large tan beta. From the hypothesis that quark and lepton masses
satisfy a classic set of relationships suggested in some Grand Unified Theories
(GUTs), we predict tan beta needs to be large, and the gluino's soft mass needs
to have the opposite sign to the wino's soft mass. Existing tools to measure
the phase of the gluino's mass at upcoming hadron colliders require
model-independent, kinematic techniques to determine the masses of the new
supersymmetric particle states. We discuss the current techniques to determine
the mass of invisible particles. We review the transverse mass kinematic
variable M_{T2} and the use of invariant-mass edges to find relationships
between masses. Next, we introduce a new technique to add additional
constraints between the masses of new particle states using M_{T2} at different
stages in a symmetric decay chain. These new relationships further constrain
the mass differences between new particle states, but still leave the absolute
mass weakly determined. Next, we introduce the constrained mass variables
M_{2C,LB}, M_{2C,UB}, M_{3C,LB}, M_{3C,UB} to provide event-by-event
lower-bounds and upper-bounds to the mass scale given mass differences. We
demonstrate mass scale determination in realistic case studies of supersymmetry
models by fitting ideal distributions to simulated data. We conclude that the
techniques introduced in this thesis have precision and accuracy that rival or
exceed the best known techniques for invisible-particle mass-determination at
hadron colliders.
