Pinching Sudakov

In this paper, we discuss the factorization of the Sudakov form factor on the Coulomb branch of maximally supersymmetric Yang-Mills theory in the near mass-shell limit. We unravel all pinch singularities of this observable making use of the Method of Regions. We find their operator content in terms of matrix elements of Wilson lines on semi-infinite and finite intervals for the jet and ultrasoft functions, respectively. However, naive factorization into these incoherent momentum components is broken at two-loop order by effects subleading in the parameter of dimensional regularization. To save the day, we perform an appropriate twisting of the functions involved as well as simultaneous finite scheme transformation of the 't Hooft coupling. Infrared physics of twisted jet and ultrasoft functions is governed by the octagon anomalous dimension, while the untwisted ultrasoft function possesses infrared evolution driven by an anomalous dimension different from the ubiquitous cusp.