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Abstract
Quantum chromodynamics (QCD) is the theory governing the interactions of quarks and gluons. When a sufficiently hard scale is present, perturbative methods of study can be used. One result of such calculations is that in the light-cone wave function of a fast moving hadron (in particular in a quarkonium, also called onium for short), the number of low momentum gluons rises fast with the onium energy. As a result, the cross section for onium-onium scattering grows rapidly and eventually violates the unitarity bound. An approach, known as the dipole formulation, allows in principle the calculation, in a certain approximation of QCD, of both the rapid rise and of the corrections (the scattering of multiple gluons in each onium) which are expected to be dominant in the restoration of unitarity; however, a full analytic treatment is not feasible. In this dissertation, a detailed study is presented of the characteristics of the onia which are important for understanding these corrections and a Monte Carlo simulation is developed for the high-energy onium evolution and for onium-onium scattering.
This allows the determination of an elastic scattering amplitude which satisfies the unitarity bound. The results show that the modification of the total cross section is relatively slow, while the alteration of the elastic cross section is much stronger. Properties of the final state are also examined, and one finds that the multiple scatterings lead to a long tail in the distribution of final state multiplicity. At even higher energies, interactions between gluons in the same onium become likely - the problem of saturation, which is much less well understood than that of multiple scattering. Tools are developed which give an indication of the effects of taking saturation into account.
