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We present analytical results for all master integrals for massless three-point functions, with one off-shell leg, at four loops. Our solutions were obtained using differential equations and direct integration techniques. We review the methods and provide additional details.

 

A bstract We present the Sudakov form factor in full color $$ \mathcal{N} $$ N = 4 supersymmetric Yang- Mills theory to four loop order and provide uniformly transcendental results for the relevant master integrals through to weight eight. 

A bstract We perform a dedicated study of the $$ q\overline{q} $$ q q ¯ -initiated two-loop electroweak-QCD Drell-Yan scattering amplitude in dimensional regularization schemes for vanishing light quark and lepton masses. For the relative order α and α s one-loop Standard Model corrections, details of our comparison to the original literature are given. The infrared pole terms of the mixed two-loop amplitude are governed by a known generalization of the dipole formula and we show explicitly that exactly the same two-loop polarized hard scattering functions are obtained in both the standard ’t Hooft-Veltman-Breitenlohner-Maison γ 5 scheme and Kreimer’s anticommuting γ 5 scheme.