Calculation of the quark and gluon form factors to three loops in QCD

By Thomas Gehrmann, E. Glover, Tobias Huber, N. Ikizlerli, C. Studerus. 2010

297 citations recorded by the source corpus.

We describe the calculation of the three-loop QCD corrections to quark and gluon form factors. The relevant three-loop Feynman diagrams are evaluated and the resulting three-loop Feynman integrals are reduced to a small set of known master integrals by using integration-by-parts relations. Our calculation confirms the recent results by Baikov et al. for the three-loop form factors. In addition, we derive the subleading $$ \mathcal{O}\left( \varepsilon \right) $$ terms for the fermion-loop type contributions to the three-loop form factors which are required for the extraction of the fermionic contributions to the four-loop quark and gluon collinear anomalous dimensions. The finite parts of the form factors are used to determine the hard matching coefficients for the Drell-Yan process and inclusive Higgs-production in soft-collinear effective theory.

Subfields: Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/3a258510238ee9aa83c34509e49bb0d9f7c56d13

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In Nuclear and High Energy Physics

Citations in the corpus

Higgs boson production at hadron colliders at N3LO in QCD (2018, methodology): “1) The renormalisation factors for the strong coupling constant and Wilson coefficient required for a computation through N(3)LO [18] are given by Zα = 1 + αS π ( −0 ǫ )”
A quasi-finite basis for multi-loop Feynman integrals (2014, background): “As a more involved example, let us consider the complete set of massless three-loop form factor integrals (their graphs are drawn, for example, in reference [25]).”
Soft triple-real radiation for Higgs production at N3LO (2013, background): “The corresponding one-loop, two-loop and three-loop amplitudes are already known in the literature as a Laurent expansion in ǫ [99–109].”
N-jettiness subtractions for NNLO QCD calculations (2015, background): “J H E P 0 9 ( 2 0 1 5 ) 0 5 8 known from the IR-finite parts of the three-loop quark and gluon form factors [98, 99].”
Color-kinematic duality for form factors (2012, background): “Moreover, the three-loop result was only obtained after the much harder QCD computation [25] (see also [26]).”
High precision determination of the gluon fusion Higgs boson cross-section at the LHC (2016, methodology): “The anomalous dimension γV can be extracted from the QCD form factor [64] and γg corresponds to the coefficient of δ(1−z) of the g → g splitting function [110].”
The full four-loop cusp anomalous dimension in N\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ \mathcal{N} $$\end{do (2019, unknown): “des. Currently, form factors relevant for the precise determination of hadron collider observables such as the Drell-Yan or Higgs boson production cross section [15, 16] are known to third loop order [17] and the advent of the next order is apparent [18–21]. Knowing the four-loop cusp anomalous dime”