Quark and Gluon Form Factors at Three Loops in Perturbative QCD

Abstract

We compute the quark and gluon form factors at up to three-loop order within massless perturbative Quantum Chromodynamics by studying the photon-quark-anti-quark vertex and the effective vertex of a Higgs boson and two gluons. We use Feynman diagram methods to derive expressions for the form-factors in terms of tensor loop integrals in dimensions. We review various methods for relating tensor integrals to a basis set of master integrals and utilize the FIRE package based on Integration-By-Parts to perform the reduction, thereby enabling the form factors to be expressed (in -dimensions) as a sum of master integrals. We assemble the known results for master integrals and use them to provide a Laurent expansion in through to . The results for the three-loop form factors may provide the building blocks for many third-order cross section calculations.