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Scattering Amplitudes via Algebraic Geometry Methods

This thesis describes recent progress in the understanding of the mathematical structure of scattering amplitudes in quantum field theory. The primary purpose is to develop an enhanced analytic framework for computing multiloop scattering amplitudes in generic gauge theories including QCD without F...

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Detalles Bibliográficos
Autor principal: Søgaard, Mads
Lenguaje:eng
Publicado: 2016
Materias:
Acceso en línea:http://cds.cern.ch/record/2224286
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author Søgaard, Mads
author_facet Søgaard, Mads
author_sort Søgaard, Mads
collection CERN
description This thesis describes recent progress in the understanding of the mathematical structure of scattering amplitudes in quantum field theory. The primary purpose is to develop an enhanced analytic framework for computing multiloop scattering amplitudes in generic gauge theories including QCD without Feynman diagrams. The study of multiloop scattering amplitudes is crucial for the new era of precision phenomenology at the Large Hadron Collider (LHC) at CERN. Loop-level scattering amplitudes can be reduced to a basis of linearly independent integrals whose coefficients are extracted from generalized unitarity cuts. We take advantage of principles from algebraic geometry in order to extend the notion of maximal cuts to a large class of two- and three-loop integrals. This allows us to derive unique and surprisingly compact formulae for the coefficients of the basis integrals. Our results are expressed in terms of certain linear combinations of multivariate residues and elliptic integrals computed from products of tree-level amplitudes. Several explicit examples are provided
id cern-2224286
institution Organización Europea para la Investigación Nuclear
language eng
publishDate 2016
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spelling cern-22242862019-09-30T06:29:59Zhttp://cds.cern.ch/record/2224286engSøgaard, MadsScattering Amplitudes via Algebraic Geometry MethodsParticle Physics - TheoryMathematical Physics and MathematicsThis thesis describes recent progress in the understanding of the mathematical structure of scattering amplitudes in quantum field theory. The primary purpose is to develop an enhanced analytic framework for computing multiloop scattering amplitudes in generic gauge theories including QCD without Feynman diagrams. The study of multiloop scattering amplitudes is crucial for the new era of precision phenomenology at the Large Hadron Collider (LHC) at CERN. Loop-level scattering amplitudes can be reduced to a basis of linearly independent integrals whose coefficients are extracted from generalized unitarity cuts. We take advantage of principles from algebraic geometry in order to extend the notion of maximal cuts to a large class of two- and three-loop integrals. This allows us to derive unique and surprisingly compact formulae for the coefficients of the basis integrals. Our results are expressed in terms of certain linear combinations of multivariate residues and elliptic integrals computed from products of tree-level amplitudes. Several explicit examples are providedCERN-THESIS-2015-365oai:cds.cern.ch:22242862016-10-13T13:32:48Z
spellingShingle Particle Physics - Theory
Mathematical Physics and Mathematics
Søgaard, Mads
Scattering Amplitudes via Algebraic Geometry Methods
title Scattering Amplitudes via Algebraic Geometry Methods
title_full Scattering Amplitudes via Algebraic Geometry Methods
title_fullStr Scattering Amplitudes via Algebraic Geometry Methods
title_full_unstemmed Scattering Amplitudes via Algebraic Geometry Methods
title_short Scattering Amplitudes via Algebraic Geometry Methods
title_sort scattering amplitudes via algebraic geometry methods
topic Particle Physics - Theory
Mathematical Physics and Mathematics
url http://cds.cern.ch/record/2224286
work_keys_str_mv AT søgaardmads scatteringamplitudesviaalgebraicgeometrymethods