A Tale Of Two Amplitudes In High Energy Theory

I will describe my work on two classes of scattering amplitudes in high energy physics. The thesis consists of two parts:one is on the proton Compton scattering in a Unified Proton-Delta theory, and the other is on the computation of scattering amplitudes in Yang-Mills theory.We study the proton Compton scattering in the first resonance region in an effective field theory approach, in an effort to better understand the proton’s electromagnetic properties, ie. its electric and magnetic polarizabilities. This part is done together with my advisor Dr. Konstantin G. Savvidy. The consistent electrodynamic interaction of the spin3/2field, which respects current conservation, has re-cently been developed by Savvidy in his generalized Rarita-Schwinger theory for the spin3/2particle, resolving the long standing superluminal propagation problem of the old Rarita-Schwinger theory. The proton and△+are naturally unified in this generalized Rarita-Schwinger theory with the proton being the spin1/2component and the△+being the spin3/2component. To describe the proton Compton scat-tering, we introduce six non-minimal electromagnetic interactions--with their coefficients being called "form factors"--and bare polarizabilities in an effective Lagrangian, consistent with the requirement of gauge invariance. We express the proton and△+magnetic moments in terms of the form factors. We then compute the proton Compton scattering amplitudes, and obtain the total electric and magnetic polariz-abilities in terms of the bare ones and the form factors. We also study an approximation of the amplitudes around the△+pole. Using experimental data, we obtain the best fit values for the form factors and bare polarizabilities. As a prediction, we derive the△+magnetic moment from the best fit values of the parameters.After some background preparation, we present our joint work with advisor Dr. Gang Chen on the study of boundary behavior of off-shell Yang-Mills amplitudes with a pair of external momenta complex-ified. In Feynman gauge, we introduce a set of "reduced vertices" which effectively capture the boundary behavior up to the first two leading orders and greatly simplify subsequent analysis. The boundary be-havior of amplitudes with two adjacent legs complexified can be read off from the reduced vertices. We then prove a theorem on the permutation sum for a given color ordering, and use it to analyze the boundary behavior of amplitudes with two non-adjacent legs complexified. Based on the boundary be-haviors, we construct off-shell Britto-Cachazo-Feng-Witten (BCFW) recursion relations for general tree level amplitudes. As applications, we calculate off-shell amplitudes 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. It is based on a previous work by Gang Chen in which the Ward identity is used to derive a recursion relation for calculating tree level boundary terms. We extend his work to derive recursion relations of the full scattering amplitudes at both tree and one loop levels. Using Feynman rules, we explicitly prove the Ward identity at tree and one loop levels. We then give recursion relations for general N-point off-shell amplitudes. We calculate three and four point one loop off-shell amplitudes as applications of our method.