Scattering Amplitudes via Algebraic Geometry Methods
Research output: Book/Report › Ph.D. thesis › Research
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Scattering Amplitudes via Algebraic Geometry Methods. / Søgaard, Mads.
The Niels Bohr Institute, Faculty of Science, University of Copenhagen, 2015. 110 p.Research output: Book/Report › Ph.D. thesis › Research
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TY - BOOK
T1 - Scattering Amplitudes via Algebraic Geometry Methods
AU - Søgaard, Mads
PY - 2015
Y1 - 2015
N2 - 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
AB - 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
UR - https://soeg.kb.dk/permalink/45KBDK_KGL/fbp0ps/alma99122138645405763
M3 - Ph.D. thesis
BT - Scattering Amplitudes via Algebraic Geometry Methods
PB - The Niels Bohr Institute, Faculty of Science, University of Copenhagen
ER -
ID: 141205168