Techniques for discoveries at the TeV scale
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Several lines of indirect evidence point to the existence of new physics at the TeV scale, corresponding to the scale set by electroweak symmetry breaking. The search for new phenomena at this scale is a major focus of current experimental efforts, encompassing a broad array of experiments including the LHC, with its current center of mass energy of 13 TeV, and dark matter direct detection experiments, sensitive to dark matter particles with masses in the GeV--TeV range. Theoretical efforts are needed to direct these searches and to interpret their results. In this dissertation, I will describe: (a) kinematic techniques for determining the masses of particles in a cascade decay that terminates in an invisible particle and the topology of the cascade; (b) a model that links dark matter with the flavor structure of the Standard Model by identifying the dark matter as the lightest component of an up-quark flavor multiplet; and (c) the unique collider signatures of a class of models containing axions of a new global symmetry that decay through mixing with Standard Model mesons.