Pinching Sudakov

TL;DR

This paper analyzes the factorization of the Sudakov form factor in maximally supersymmetric Yang-Mills theory on the Coulomb branch, revealing the structure of pinch singularities and the effects of two-loop corrections.

Contribution

It uncovers the operator content of pinch singularities using the Method of Regions and introduces a scheme for factorization involving twisting and finite scheme transformations.

Findings

Pinch singularities are characterized by Wilson line matrix elements.

Naive factorization breaks down at two-loop order due to subleading effects.

Infrared physics is governed by the octagon anomalous dimension and a distinct ultrasoft anomalous dimension.

Abstract

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.