Three-Loop Gluon Scattering in QCD and the Gluon Regge Trajectory.

We compute the three-loop helicity amplitudes for the scattering of four gluons in QCD. We employ projectors in the 't Hooft-Veltman scheme and construct the amplitudes from a minimal set of physical building blocks, which allows us to keep the computational complexity under control. We obtain relatively compact results that can be expressed in terms of harmonic polylogarithms. In addition, we consider the Regge limit of our amplitude and extract the gluon Regge trajectory in full three-loop QCD. This is the last missing ingredient required for studying single-Reggeon exchanges at next-to-next-to-leading logarithmic accuracy.

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.

Diphoton Amplitudes in Three-Loop Quantum Chromodynamics.

We consider the three-loop scattering amplitudes for the production of a pair of photons in quark-antiquark annihilation in QCD. We use suitably defined projectors to efficiently calculate all helicity amplitudes. We obtain relatively compact analytic results that we write in terms of harmonic polylogarithms or, alternatively, multiple polylogarithms of up to depth three. This is the first calculation of a three-loop four-point scattering amplitude in full QCD.

Two-Loop Helicity Amplitudes for Diphoton Plus Jet Production in Full Color.

We present the two-loop QCD amplitudes for the production of two photons and a jet at hadron colliders with full-color dependence. This is the first time that radiative corrections for a five-particle scattering process have been computed beyond the leading-color approximation at this perturbative order in QCD. The results presented in this Letter will be crucial to guaranteeing reliable predictions with unprecedented precision for diphoton production at hadron colliders. The methodologies that we describe lead to a significant simplification of the calculation and their applicability extends to a wider range of five-point scattering processes.

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.