Some topics in the calculation of QCD hard scattering processes

We have studied the single effective subprocess approximation for two-jet events at large transverse momentum. This strongly suggested a factorized form for the cross-section for producing two jet events in pp and pp interactions in terms of an effective structure function and single basic subprocesses. Also the single and two-jet fractions which are based on the effective structure function have been studied and it is shown that the contribution of these fractions in pp and pp interactions are independent of the jet angular distribution. We then tried to explain the surprising similarity between the angular distributions of different 2 → 3 QCD parton-parton subprocesses in the transverse plane. This feature turns out to be associated with an exact relationship between Altarelli-Parisi splitting kernels. Our results are published in Phys. Lett. B212 (1988), 95.The second part of our work is to handle the calculation of the matrix element squared for six-gluon scattering to the leading order in the number of colours and a compact expression was obtained in terms of kinematical variables. This resulted in Durham preprint DTP 88/40 (1989). We developed a powerful technique which strongly suggested a factorized form for the non-leading terms. Together with the leading expression, this gave the exact matrix element squared for the six- gluon scattering for the first time represented analytically in terms of kinematical invariants in a compact form. Finally we examined how the non-leading terms are growing in importance when one increases the number of gluons in multi-gluon scattering.