Abstract In this thesis I explore three hard processes where QCD plays a major role. In the first problem, different hard nuclear processes are investigated for the possible measurement of the quadrupole gluon distribution, which exists only for hadrons with spin â‰¥ 1. Choosing Li3 as a typical light nucleus I use the convolution model and a QCD inspired parton recombination model to calculate cross section asymmetries. The effects of an exotic quadrupole gluon component upon asymmetries in prompt photon production and J/ Ïˆ leptoproduction are estimated. The calculated asymmetries are quite large even though the corresponding cross sections are very small. This raises the hope that this quadrupole asymmetry can ultimately be measured. The second problem deals with the decay of hadrons, in particular Upsilon decay, which is one of the first applications of QCD and provides a testbench to study many ideas of QCD. Since it is possible to measure the photon spectrum in the decay Î³r + 2g, one can test a theory against many data points. This is in contrast to the prediction of total decay rate which is a single number. I use a systematic gaugeinvariant method, which starts directly from QCD and allows for an expansion in the quark relative velocity 'U, a small natural parameter for heavy quark systems. This technique is used to calculate the rate for an upsilon meson to decay inclusively into a prompt photon. It is found that the inclusion of these O ( v2) corrections tends to incase the photon rate in the middle z range and to lower it for larger z, a feature supported by the data. In the third, and last problem, I calculate the fragmentation function for a charm quark to decay inclusively into Swave charmonium states, including relativistic and binding energy collections in powers of the quark relative velocity v. In this case the direct introduction of a gaugelink operator provides a quick route to arriving at gauge invariant matrix elements. I also use these fragmentation functions to estimate their contribution to the production rate of nc and J / Ïˆ Z0 decay. These corrections contribute about 38% to the integrated c J/ Ïˆ+X fragmentation. For nc these are found to be small.
