Feynman integrals for five-point two-loop one-mass amplitudes in QCD

Abstract: The energy reach and anticipated data of the Large Hadron Collider (LHC) at CERN will allow precision tests of the Standard Model and New Physics searches. In this thesis we contribute to crucial theory predictions for these quests. We obtain the two-loop five-point Feynman integrals with one massive external leg, and massless virtual particles. These play an important role for the theory predictions of Z- and W-boson production in association with two jets in Quantum Chromodynamics (QCD), as well as the production of a Higgs-boson in association with two jets in the large top-mass approximation. The main result of this thesis is the computation of the full set of planar fiveve-point integrals as well as three distinct non-planar hexa-box topologies. The computation was done by setting up frst-order differential equations for the Feynman integrals, which are solved in a second step. We found the canonical basis of 'pure' Feynman integrals, which simplifies their dependence on the dimensional regulator and allows for effi- cient solution of the differential equation. We identify the algebraic kinematic dependence of the differential equation, given by the so-called symbol alphabet which determines the function's analytic properties. Ansatz techniques, based on universal properties of Feynman integrals, are applied to allow for the construction of the analytic differential equation from a small number of numerical evaluations. This technique circumvents the main bottleneck in Feynman integral computation originating in large linear systems in six parameters. Such systems appear in the integration-by-parts identities relating generic Feynman integrals to the basis. We integrate the canonical differential equation numerically using the generalized power-series approach and provide high-precision numerical values for all integrals in all kinematic regions. Moreover, for the planar integrals we performed a dedicated study of the computation-time requirements and con- firmed the efficiency of the numerical integration

Object Details

• Location: Deutsche Nationalbibliothek Frankfurt am Main
• Extent: Online-Ressource
• Language: Englisch
• Notes: Universität Freiburg, Dissertation, 2021

Classification and Topics

• Classification: Physik
• Keyword: Zweischleifenintegral

Contributors, Places and Time

• Event: Veröffentlichung
• (where): Freiburg
• (who): Universität
• (when): 2022
• Creator: Tschernow, Wladimir
• Contributor: Ita, Harald ; Dittmaier, Stefan ; Albert-Ludwigs-Universität Freiburg. Fakultät für Mathematik und Physik

Further information

• DOI: 10.6094/UNIFR/226386
• URN: urn:nbn:de:bsz:25-freidok-2263866
• Rights: Open Access; Der Zugriff auf das Objekt ist unbeschränkt möglich.
• Last update: 15.08.2025, 7:34 AM CEST