The nonplanar cusp and collinear anomalous dimension at four loops in $\mathcal{N}=4$ SYM theory

Abstract

We present numerical results for the nonplanar lightlike cusp and collinear anomalous dimension at four loops in $\mathcal{N}=4$ SYM theory, which we infer from a calculation of the Sudakov form factor. The latter is expressed as a rational linear combination of uniformly transcendental integrals for arbitrary colour factor. Numerical integration in the nonplanar sector reveals explicitly the breakdown of quadratic Casimir scaling at the four-loop order. A thorough analysis of the reported numerical uncertainties is carried out.

Comments: 10 pages, 2 figures, 1 table. Proceedings of the 13th International Symposium on Radiative Corrections (Applications of Quantum Field Theory to Phenomenology), 25-29 September, 2017, St. Gilgen, Austria