It is found experimentally that total cross sections increase with energy. Partonic total cross sections can be calculated in perturbative QCD provided the coupling constant is small, though multiloop diagrams must be included at high energies. Such calculations are difficult and can usually be carried out only in the leading-log approximation. The resulting BFKL Pomeron violates the Froissart bound, which forbids total cross sections asymptotically to grow faster than the square of the logarithm of energy. To restore unitarity and the Froissart bound, subleading contributions of all orders must be included. Unfortunately existing techniques for computing Feynman diagrams prove to be inadequate for this difficult task. The purpose of this thesis is to develop new techniques capable of solving this problem. Since factorization in the impact-parameter space is a main ingredient needed to reach unitarity, such a technique must be capable of implementing factorization in an efficient way. We introduce the non-abelian cut diagrams for that purpose. We use it to compute quark-quark scattering amplitude to the two-loop order and show how the new technique can overcome the inadequacies of the existing method. We are also able to use this method to prove factorization of a class of Feynman diagrams, which we shall refer to as 's-channel ladder diagrams', though the proof of general factorization is not attempted in this thesis. We have also developed a more efficient method to calculate the high-energy dependences of individual Feynman and non-abelian cut diagrams. This method relies on a systematic study of the paths used by momenta to flow through the diagram, and will thus be referred to as the path method for flow diagrams. These new techniques can be used to implement unitarity and to restore the Froissart bound, but this final goal is not carried out here.
| Identifer | oai:union.ndltd.org:LACETR/oai:collectionscanada.gc.ca:QMM.36588 |
| Date | January 1999 |
| Creators | Feng, Yongjian, 1969- |
| Publisher | McGill University |
| Source Sets | Library and Archives Canada ETDs Repository / Centre d'archives des thèses électroniques de Bibliothèque et Archives Canada |
| Language | English |
| Detected Language | English |
| Type | Electronic Thesis or Dissertation |
| Format | application/pdf |
| Coverage | Doctor of Philosophy (Department of Physics.) |
| Rights | All items in eScholarship@McGill are protected by copyright with all rights reserved unless otherwise indicated. |
| Relation | alephsysno: 001763293, proquestno: NQ64557, Theses scanned by UMI/ProQuest. |
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