Infrared singularities in the high-energy limit

TL;DR

This paper analyzes the infrared singularity structure of gauge theory amplitudes in the high-energy limit, providing a general expression for soft and collinear divergences and examining the validity of Reggeization at different logarithmic orders.

Contribution

It introduces a universal formula for infrared divergences in the high-energy limit and investigates the breakdown of simple Reggeization at NNLL order.

Findings

Proves leading-logarithmic Reggeization for infrared divergences.

Shows Regge cuts appear at NNLL level, breaking simple Reggeization.

Constrains possible three-loop corrections to the dipole formula.

Abstract

We use our current understanding of the all-order singularity structure of gauge theory amplitudes to probe their high-energy limit. Our starting point is the dipole formula, a compact ansatz for the soft anomalous dimension matrix of massless multi-particle amplitudes. In the high-energy limit, we find a simple and general expression for the infrared factor generating all soft and collinear singularities of the amplitude, which is valid to leading power in $|t|/s$ and to all logarithmic orders. This leads to a direct and general proof of leading-logarithmic Reggeization for infrared divergent contributions to the amplitude. Furthermore, we can prove explicitly that the simplest form of Reggeization, based on the absence of Regge cuts in the complex angular momentum plane, breaks down at the NNLL level. Finally, we note that the known features of the high-energy limit can be used to constrain possible corrections to the dipole formula, starting at the three-loop order.