We compute the quark and gluon form factors at up to three-loop order within massless perturbative Quantum Chromodynamics by studying the photon-quark-anti-quark vertex and the effective vertex of a Higgs boson and two gluons. We use Feynman diagram methods to derive expressions for the form-factors in terms of tensor loop integrals in $D=4-2\epsilon$ dimensions. We review various methods for relating tensor integrals to a basis set of master integrals and utilize the FIRE package based on Integration-By-Parts to perform the reduction, thereby enabling the form factors to be expressed (in $D$-dimensions) as a sum of master integrals. We assemble the known results for master integrals and use them to provide a Laurent expansion in $\epsilon$ through to $\mathcal{ O}(\epsilon^{0})$. The results for the three-loop form factors may provide the building blocks for many third-order cross section calculations.
| Identifer | oai:union.ndltd.org:bl.uk/oai:ethos.bl.uk:512884 |
| Date | January 2009 |
| Creators | Ikizlerli, Nehir |
| Publisher | Durham University |
| Source Sets | Ethos UK |
| Detected Language | English |
| Type | Electronic Thesis or Dissertation |
| Source | http://etheses.dur.ac.uk/118/ |
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