Matter dependence of the four-loop cusp anomalous dimension

Abstract

We compute analytically the matter-dependent contributions to the quartic Casimir term of the four-loop light-like cusp anomalous dimension in QCD, with $n_f$ fermion and $n_s$ scalar flavours. 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 whose integrands have a dlog 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 $\mathcal{N}=4$ super Yang-Mills theory.

7 pages, 3 figures, 1 table, journal version

References in corpus (13)

• Algorithm FIRE -- Feynman Integral REduction
• Thrust at N^3LL with Power Corrections and a Precision Global Fit for alphas(mZ)
• A precise determination of alpha_s from LEP thrust data using effective field theory
• Scattering amplitudes over finite fields and multivariate functional reconstruction
• Four-Loop Non-Singlet Splitting Functions in the Planar Limit and Beyond
• Large-nf Contributions to the Four-Loop Splitting Functions in QCD
• On the Singularity Structure of Maximally Supersymmetric Scattering Amplitudes
• A Precise Determination of ${\alpha }_s$ from the C-parameter Distribution
• Quark and gluon form factors to four loop order in QCD: the $N_f^3$ contributions
• The $n_f^2$ contributions to fermionic four-loop form factors
• Four-loop quark form factor with quartic fundamental colour factor
• Simple loop integrals and amplitudes in N=4 SYM
• The {\tt Mathematica} package {\tt TopoID} and its application to the Higgs boson production cross section

Cited by in corpus (4)

• FiniteFlow: multivariate functional reconstruction using finite fields and dataflow graphs
• The Fully-Differential Gluon Beam Function at NNLO
• Resummed inclusive cross-section in Randall-Sundrum model at NNLO+NNLL
• On-shell Methods for Form Factors in N=4 SYM and Their Applications