Quark Mass Generation and Mixing; and the Next To-Leading Order QCD Calculation for Hadron-Hadron Elastic Collisions.

This thesis is arranged in two distinct parts. The first part involves the construction of a novel dynamical scheme which is capable of generating the masses of the quarks and the elements of the Kobayashi-Maskawa matrix, and which does not rely upon the Higgs mechanism. The up quarks acquire their masses by coupling to a new heavy fermion via emission and reabsorption of a new scalar boson. The down quarks, on the other hand, obtain their masses via a correction to the up mass matrix as a result of an anomalous flavour changing interaction of the W^+/- . Extensions of the mass generation model are proposed and discussed. The second part involves the leading-log s study of hadron-hadron elastic scattering to order alpha_{s}^3. By introducing wave functions, it is found that there are three types of form factor for the proton, and two for the pion. These form factors turn out to cancel the infrared divergence which occurs in quark-quark scattering. To this order in alpha_{s}, the amplitude of such elastic scattering is shown to have the form ~(1 + log(s)(alpha _{o} + alpha^ ' t + O(t^2)) for the imaginary part and a constant ~alpha _{odd} for the real part, where s and t are the usual Mandelstam variables, and the alpha's are constants.