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A Tale Of Two Amplitudes In High Energy Physics

(abbreviated) I will describe my work on proton Compton scattering in a Unified Proton-Delta theory and on the computation of scattering amplitudes in Yang-Mills theory. We study proton Compton scattering in the first resonance region in an effective field theory approach with adviser Dr. Konstantin G. Savvidy. Proton and $Δ^+$ are naturally unified in the generalized Rarita-Schwinger theory proposed by Savvidy. We introduce six non-minimal electromagnetic interactions--with their coefficients being called "form factors"--and bare polarizabilities in an effective Lagrangian. We express proton and Delta magnetic moments and the electromagnetic polarizabilities in terms of the bare polarizabilities and the form factors. We fit the form factors and bare polarizabilities using experimental data and derive Delta magnetic moment from the best fit values of the parameters. Then I present our joint work with adviser Dr. Gang Chen on the study of boundary behavior of off-shell Yang-Mills amplitudes with a pair of external momenta complexified. In Feynman gauge, we introduce a set of "reduced vertices" which can capture the boundary behavior up to the first two leading orders. We then prove a theorem on permutation sum for a given color ordering, and use it to analyze the boundary behavior of amplitudes with two non-adjacent legs complexified. Then we construct off-shell Britto-Cachazo-Feng-Witten (BCFW) recursion relations and study relations between off-shell amplitudes. Finally, we study the recursion relations for off-shell Yang-Mills amplitudes at tree and one loop levels as deduced from imposing complexified Ward identity, also in collaboration with Dr. Gang Chen.