Standard methods for performing analytic perturbative calculations for the process of <i>e</i><sup>+</sup><i>e</i><sup>-</sup> → <i>q? </i>up to ?(<i>α<sub>s</sub></i>) are explained and results given. An emphasis is given to the organisation calculations using the Cutkosky cutting rules and the renormalisation of the massive quark propagator. Methods for numerical integration are presented including those used in VEGAS. The numerical methods used in the Beowulf program for calculating infra-red safe observables for jet events from electron-positron collisions are also explained. Cancellations of singularities required for numerical calculations are demonstrated using an example in ?<sup>3</sup> theory both numerically and graphically. Renormalisation by subtraction of appropriate integrals is also covered. Adaptations of the Beowulf procedure required for the inclusion of massive fermions are developed and explained. An alternative method for including the quark self energy and its related cuts using scalar decomposition, numerically equivalent integrals and its spinor structure is introduced. The methods are used to calculate the ?(<i>α<sub>s</sub></i>) corrections to the process <i>e</i><sup>+</sup><i>e</i><sup>-</sup> → <i>q? </i>using VEGAS. Drawbacks of the smearing function required in the numerical integration due to the corrections dependence on the mass and centre of mass energy are discussed. Results of the ?(<i>α<sub>s</sub></i>) cross section using the numerical method verify the procedure. The method was then used to see the effects of mass on the thrust distribution and when using the Durham and JADE jet algorithms.
| Identifer | oai:union.ndltd.org:bl.uk/oai:ethos.bl.uk:660918 |
| Date | January 2004 |
| Creators | Ramtohul, Mark Anthony Sookraj |
| Publisher | University of Edinburgh |
| Source Sets | Ethos UK |
| Detected Language | English |
| Type | Electronic Thesis or Dissertation |
| Source | http://hdl.handle.net/1842/12831 |
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