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We compute the full-color two-loop five-gluon amplitude for the all-plus helicity configuration. In order to achieve this, we calculate the required master integrals for all permutations of the external legs, in the physical scattering region. We verify the expected divergence structure of the amplitude and extract the finite hard function. We further validate our result by checking the factorization properties in the collinear limit. Our result is fully analytic and valid in the physical scattering region. We express it in a compact form containing logarithms, dilogarithms, and rational functions.

We compute analytically the matter-dependent contributions to the quartic Casimir term of the four-loop lightlike cusp anomalous dimension in QCD, with n_{f} fermion and n_{s} scalar flavors. The result is extracted from the double pole of a scalar form factor. We adopt a new strategy for the choice of master integrals with simple analytic and infrared properties, which significantly simplifies our calculation. To this end, we first identify a set of integrals for which the integrands have a d log form, and are hence expected to have uniform transcendental weight. We then perform a systematic analysis of the soft and collinear regions of loop integration and build linear combinations of integrals with a simpler infrared pole structure. In this way, only integrals with ten or fewer propagators are needed for obtaining the cusp anomalous dimension. These integrals are then computed via the method of differential equations through the addition of an auxiliary scale. Combining our result with that of a parallel paper, we obtain the complete n_{f} dependence of the four-loop cusp anomalous dimension in QCD. Finally, using known numerical results for the gluonic contributions, we obtain an improved numerical prediction for the cusp anomalous dimension in N=4 super Yang-Mills theory.

We compute the leading-color contributions to five-gluon scattering at two loops in massless QCD. The integrands of all independent helicity amplitudes are evaluated using d-dimensional generalized unitarity cuts and finite field reconstruction techniques. Numerical evaluation of the integral basis is performed with sector decomposition methods to obtain the first benchmark results for all helicity configurations of a 2→3 scattering process in QCD.

We give an introduction to several regularization schemes that deal with ultraviolet and infrared singularities appearing in higher-order computations in quantum field theories. Comparing the computation of simple quantities in the various schemes, we point out similarities and differences between them.

Small- x logarithmic enhancements arising from high-energy gluon emissions affect both the evolution of collinearly-factorized parton densities and partonic coefficient functions. With the higher collider energy reached by the LHC, the prospect of a future high-energy collider, and the recent deep-inelastic scattering (DIS) results at small- x from HERA, providing phenomenological tools for performing small- x resummation has become of great relevance. In this paper we discuss a framework to perform small- x resummation for both parton evolution and partonic coefficient functions and we describe its implementation in a computer code named High-Energy Large Logarithms (HELL). We present resummed and matched results for the DGLAP splitting functions and, as a proof of principle, for the massless structure functions in DIS. Furthermore, we discuss the uncertainty from subleading terms on our results.

We present the calculation of the cross section for Higgs boson production in association with a top quark pair plus one jet, at next-to-leading-order accuracy in QCD. All mass dependence is retained without recurring to any approximation. After including the complete next-to-leading-order QCD corrections, we observe a strong reduction in the scale dependence of the result. We also show distributions for the invariant mass of the top quark pair, with and without the additional jet, and for the transverse momentum and the pseudorapidity of the Higgs boson. Results for the virtual contributions are obtained with a novel reduction approach based on integrand decomposition via the Laurent expansion, as implemented in the library, NINJA. Cross sections and differential distributions are obtained with an automated setup which combines the GOSAM and SHERPA frameworks.

We report on the calculation of the cross section for Higgs boson production in association with three jets via gluon fusion, at next-to-leading-order (NLO) accuracy in QCD, in the infinite top-mass approximation. After including the complete NLO QCD corrections, we observe a strong reduction in the scale dependence of the result, and an increased steepness in the transverse momentum distributions of both the Higgs boson and the leading jets. The results are obtained with the combined use of GOSAM, SHERPA, and the MADDIPOLE-MADEVENT framework.