Effective Field Theory Approaches to Particle Physics Beyond the Standard Mode

This dissertation covers applications of effective field theory (EFT) ideas and techniques to the study of particle physics beyond the Standard Model (SM). The recent discovery of the Higgs boson without other new physics discoveries hints at the possibility that additional exotic states that couple to SM particles, if they exist, are not in the neighborhood of the electroweak scale. In this case, precision measurements of SM processes offer an important indirect probe of heavy new physics that is complementary to direct searches for new particles at high energy colliders, and EFT becomes the tool of choice to bridge a vast range of new physics ideas and experimental observation.;We start with a discussion of the precision analyses program, reviewing the analysis framework and the status of electroweak precision tests. The Higgs boson discovery has added a new module to this program, and we point out new issues related to heavy quark masses that must be taken into account in future precision studies of the Higgs boson.;Various approaches exist in the literature to extract information about new physics from precision analyses. Two examples are oblique parameters and triple gauge couplings (TGCs). We critically examine these conventional approaches in the EFT framework. In particular, we clarify that the applicability of oblique parameters is restricted to universal theories at leading order, and we find that TGCs no longer serve as a general parameterization of new physics effects in W boson pair production with recent LHC data. In both cases, EFT provides a consistent framework to rectify and extend the oversimplified conventional approaches, in order to take full advantage of high energy data to learn about new physics.;We next turn to the subject of EFT matching, i.e. deriving a low energy EFT by integrating out heavy degrees of freedom from an ultraviolet theory. We develop a diagrammatic framework to carry out covariant functional matching calculations in a systematic manner. In contrast to conventional Feynman diagram methods, our approach avoids the detour of computing correlation functions, and meanwhile preserves gauge covariance and simplifies calculations. Finally, we apply this new technique to trans-TeV supersymmetry, and show that future precision Higgs measurements can probe scenarios of Yukawa unification featuring heavy superpartners beyond direct LHC reach.