Quark and Gluon Form Factors in Four-Loop QCD.

We compute the photon-quark and Higgs-gluon form factors to four-loop order within massless perturbative quantum chromodynamics. Our results constitute ready-to-use building blocks for N^{4}LO cross sections for Drell-Yan processes and gluon-fusion Higgs boson production at the LHC. We present complete analytic expressions for both form factors and show several of the most complicated master integrals.

Cusp and Collinear Anomalous Dimensions in Four-Loop QCD from Form Factors.

We calculate the complete quark and gluon cusp anomalous dimensions in four-loop massless QCD analytically from first principles. In addition, we determine the complete matter dependence of the quark and gluon collinear anomalous dimensions. Our approach is to Laurent expand four-loop quark and gluon form factors in the parameter of dimensional regularization. We employ finite field and syzygy techniques to reduce the relevant Feynman integrals to a basis of finite integrals, and subsequently evaluate the basis integrals directly from their standard parametric representations.