Universal structure of subleading infrared poles in gauge theory amplitudes

TL;DR

This paper investigates the origin of subleading infrared poles in gauge theory amplitudes, revealing a universal structure governed by a single function related to the gauge theory's matrix elements, with implications for conformal theories.

Contribution

It identifies a universal function G(alpha_s) that captures subleading infrared poles in gauge theory form factors, linking it to gauge-theory matrix elements and factorization properties.

Findings

Subleading poles originate from a universal function G(alpha_s).

G(alpha_s) combines a universal eikonal anomalous dimension, a non-eikonal term, and a process-dependent coefficient.

In conformal theories, a simple relation exists between the form factor and the cusp anomalous dimension.

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(alpha_s), depending on both the spin and gauge quantum numbers of the field. We relate G(alpha_s) to gauge-theory matrix elements involving the gluon field strength. We then show that G(alpha_s) is the sum of three terms: a universal eikonal anomalous dimension, a universal non-eikonal contribution, given by the coefficient B_delta (alpha_s) of delta(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_delta (alpha_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.