In this thesis, we apply techniques from effective field theory to examine two contemporary problems in particle physics at two different scales. At low energies, recent experiments have indicated that the proton is smaller than previously measured. As the proton is a composite particle, we do not have a fundamental quantum field theory to describe its interactions with the electromagnetic field. An effective Lagrangian can be constructed by considering all relevant symmetries at low energies, and this description can be used to consistently compute higher-order corrections to proton structure as measured by bound state spectroscopy and lepton-nucleon scattering.;At high energies, the Higgs mass has been measured to be close to the weak scale and the current determinations of its couplings are consistent with those predicted by the Standard Model (SM). However, if the SM is indeed the correct description of nature up to Planck scales, the Higgs mass is subject to large quantum corrections. In a large class of supersymmetric models, the scalar partners of the SM fermions stabilize the Higgs mass against these corrections and the measured value of the Higgs mass can be accommodated; however, no particles except the Higgs have yet been found at the LHC, which indicates a heavy spectrum of superpartners. If there is a separation of scales, we can view the SM as the effective theory and use renormalization group evolution, together with the measured Higgs mass, to determine the range of scales at which these superpartners may lie.
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