Universal structure of subleading infrared poles in gauge theory amplitudes

Abstract

We study the origin of subleading soft and collinear poles of form factors and amplitudes in dimensionally-regulated massless gauge theories. In the case of form factors of fundamental fields, these poles originate from a single function of the coupling, denoted G(α s ), depending on both the spin and gauge quantum numbers of the field. We relate G(α s ) to gauge-theory matrix elements involving the gluon field strength. We then show that G(α s ) is the sum of three terms: a universal eikonal anomalous dimension, a universal non-eikonal contribution, given by the coefficient B δ (α s ) of δ(1−z) in the collinear evolution kernel, and a process-dependent short-distance coefficient function, which does not contribute to infrared poles. Using general results on the factorization of soft and collinear singularities in fixed-angle massless gauge theory amplitudes, we conclude that all such singularities are captured by the eikonal approximation, supplemented only by the knowledge of B δ (α s ). We explore the consequences of our results for conformal gauge theories, where in particular we find a simple exact relation between the form factor and the cusp anomalous dimension.

From webs to polylogarithms

“…Corrections to the dipole formula may first appear at three loops, from diagrams involving four Wilson lines. Despite recent progress [35][36][37][38][39][40][86][87][88][89][90][91][92], it seems that general considerations fall short of excluding or fixing these corrections; 1 further input from explicit calculations is needed. This motivates the present work, which is part of a larger project aimed at determining the anomalous dimension at three-loop order, and understanding its structure to all orders.…”

Gauge theory webs and surfaces

“…When renormalized by the minimal subtraction of ultraviolet poles, the exponent E can be written in the form [37],…”

“…Equation (7) gives all the poles of the cusp, when reexpanded in terms of the coupling at any fixed scale. We note that for timelike kinematics, the renormalization scale µ 2 should be chosen negative [37].…”

Space-like (vs. time-like) collinear limits in QCD: is factorization violated?

“…In the context of dimensional regularization, the (virtual) IR divergences of QCD amplitudes have been studied [1,2,3,4,5,6,7,8] at one-loop, two-loop and higher-loop orders. The singularity structure related to (single and multiple) soft-parton radiation has been explicitly worked out [9,10,11,12,13,14] in the cases of tree-level, one-loop and two-loop scattering amplitudes.…”