Calculations in Quantum Chromodynamics

The author analyzes two problems which extend the predictive ability of Quantum Chromodynamics. He studies composite operators in lattice gauge theory that reduce to operators of the form anti psi gamma DDDD ... psi in the continuum limit; such operators arise in perturbative analyses of quantum chromodynamics. Using these results and the data of a numerical simulation one could normalize exclusive processes and predict moments of deep inelastic scattering structure functions. To initiate the program the author constructs and renormalizes lattice operators to the one-loop level. He is encouraged that the hadronic matrix elements of the simpler operators are within reach of numerical simulations. The author also calculates a corrected photon spectrum in the endpoint region, z → 1, for direct photon decay of the upsilon by summing the leading logarithms of (1-z) to all orders in perturbation theory. This effect causes the cross section to level out at approx. = = .8, removing the sharp peak in the tree level prediction, but does not cause the cross section to turn over