Neutrino Oscillations, And Hadronic Physics When Considering A Large Number Of Colors In Quantum Chromodynamics

This document consists of three chapters. The first chapter includes a detailed description of neutrino oscillations with an emphasis on the naturalness of obtaining a small value Ue3 within the Maki-Nakagawa-Sakata mixing matrix. With the use of the seesaw mechanism, it is found that the upper bound on this particular element is approaching its lower limit when we assume a very natural set of criteria for the origins of leptonic mixing. Also obtained are some general expressions which could provide insight into the Majorana nature of neutrino oscillations. The second chapter explores the use of operator methods in a 1/ Nc expansion for magnetic moments in QCD. An analysis of the entire set of magnetic moments is provided, including an explicit calculation of all twenty seven corresponding operators. A prediction of the sixteen unknown magnetic moments is also given, which were found using only the Wigner-Eckart theorem and a simple least squares fit to the available data. Using the predicted magnetic moments, we were also able to predict the six radiative decay widths corresponding to the Σ*+, Σ *0, Ξ*0, and Ξ*−. In the third chapter; using a formalism established to include systematic corrections to the leading order S- matrix elements, we derive expressions for the pion photoproduction amplitudes in the 1/Nc expansion of QCD, and obtain linear relations directly from this expansion that relate electromagnetic multipole amplitudes at all energies. The leading-order relations in 1/Nc compare favorably with available data, while the next-to-leading order relations seem to provide only a small improvement. However, when resonance parameters are compared directly, the agreement at O(1/Nc) or O(1/ N2c ) is impressive