NLO Rutherford Scattering and the Kinoshita-Lee-Nauenberg Theorem

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dc.contributor.advisorHorowitz, William Aen_ZA
dc.contributor.authorIbrahim, Abdullah Khalil Hassanen_ZA
dc.date.accessioned2017-09-01T14:21:23Z
dc.date.available2017-09-01T14:21:23Z
dc.date.issued2017en_ZA
dc.description.abstractWe calculate to next-to-leading order accuracy the high-energy elastic scattering cross section for an electron off of a classical point source. We use the MS renormalization scheme to tame the ultraviolet divergences while the infrared singularities are dealt with using the well known Kinoshita-Lee-Nauenberg theorem. We show for the first time how to correctly apply the Kinoshita-Lee-Nauenberg theorem diagrammatically in a next-to-leading order scattering process. We improve on previous works by including all initial and final state soft radiative processes, including absorption and an infinite sum of partially disconnected amplitudes. Crucially, we exploit the Monotone Convergence Theorem to prove that our delicate rearrangement of this formally divergent series is uniquely correct. This rearrangement yields a factorization of the infinite contribution from the initial state soft photons that then cancels in the physically observable cross section. Since we use the MS renormalization scheme, our result is valid up to arbitrarily large momentum transfers between the source and the scattered electron as long as α log(1/δ) << 1 and α log(1/δ) log(Δ/E) << 1, where Δ and δ are the experimental energy and angular resolutions, respectively, and E is the energy of the scattered electron. Our work aims at computing the NLO corrections to the energy loss of a high energetic parton propagating in a quark-gluon plasma.en_ZA
dc.identifier.apacitationIbrahim, A. K. H. (2017). <i>NLO Rutherford Scattering and the Kinoshita-Lee-Nauenberg Theorem</i>. (Thesis). University of Cape Town ,Faculty of Science ,Department of Physics. Retrieved from http://hdl.handle.net/11427/25027en_ZA
dc.identifier.chicagocitationIbrahim, Abdullah Khalil Hassan. <i>"NLO Rutherford Scattering and the Kinoshita-Lee-Nauenberg Theorem."</i> Thesis., University of Cape Town ,Faculty of Science ,Department of Physics, 2017. http://hdl.handle.net/11427/25027en_ZA
dc.identifier.citationIbrahim, A. 2017. NLO Rutherford Scattering and the Kinoshita-Lee-Nauenberg Theorem. University of Cape Town.en_ZA
dc.identifier.ris TY - Thesis / Dissertation AU - Ibrahim, Abdullah Khalil Hassan AB - We calculate to next-to-leading order accuracy the high-energy elastic scattering cross section for an electron off of a classical point source. We use the MS renormalization scheme to tame the ultraviolet divergences while the infrared singularities are dealt with using the well known Kinoshita-Lee-Nauenberg theorem. We show for the first time how to correctly apply the Kinoshita-Lee-Nauenberg theorem diagrammatically in a next-to-leading order scattering process. We improve on previous works by including all initial and final state soft radiative processes, including absorption and an infinite sum of partially disconnected amplitudes. Crucially, we exploit the Monotone Convergence Theorem to prove that our delicate rearrangement of this formally divergent series is uniquely correct. This rearrangement yields a factorization of the infinite contribution from the initial state soft photons that then cancels in the physically observable cross section. Since we use the MS renormalization scheme, our result is valid up to arbitrarily large momentum transfers between the source and the scattered electron as long as α log(1/δ) << 1 and α log(1/δ) log(Δ/E) << 1, where Δ and δ are the experimental energy and angular resolutions, respectively, and E is the energy of the scattered electron. Our work aims at computing the NLO corrections to the energy loss of a high energetic parton propagating in a quark-gluon plasma. DA - 2017 DB - OpenUCT DP - University of Cape Town LK - https://open.uct.ac.za PB - University of Cape Town PY - 2017 T1 - NLO Rutherford Scattering and the Kinoshita-Lee-Nauenberg Theorem TI - NLO Rutherford Scattering and the Kinoshita-Lee-Nauenberg Theorem UR - http://hdl.handle.net/11427/25027 ER - en_ZA
dc.identifier.urihttp://hdl.handle.net/11427/25027
dc.identifier.vancouvercitationIbrahim AKH. NLO Rutherford Scattering and the Kinoshita-Lee-Nauenberg Theorem. [Thesis]. University of Cape Town ,Faculty of Science ,Department of Physics, 2017 [cited yyyy month dd]. Available from: http://hdl.handle.net/11427/25027en_ZA
dc.language.isoengen_ZA
dc.publisher.departmentDepartment of Physicsen_ZA
dc.publisher.facultyFaculty of Scienceen_ZA
dc.publisher.institutionUniversity of Cape Town
dc.subject.otherTheoretical Physicsen_ZA
dc.titleNLO Rutherford Scattering and the Kinoshita-Lee-Nauenberg Theoremen_ZA
dc.typeMaster Thesis
dc.type.qualificationlevelMasters
dc.type.qualificationnameMScen_ZA
uct.type.filetypeText
uct.type.filetypeImage
uct.type.publicationResearchen_ZA
uct.type.resourceThesisen_ZA
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