Next-to-soft corrections to high energy scattering in QCD and gravity

TL;DR

This work extends the Regge limit analysis of 2→2 scattering in QCD and gravity to next-to-soft order, using generalized Wilson lines to systematically include external and internal emissions. In QCD, NE corrections evaluate to a power-suppressed, collinearly singular contribution to the Regge trajectory that can be absorbed into external impact factors; in gravity, NE corrections yield two independent deflection angles, matching classical expectations for test particles in the field of the other, and supporting a gravity–gauge double-copy interpretation. The results show that, at NE order, the calculations for QCD and gravity are structurally parallel and can be related by double-copy replacements at the integrand level. The study also reveals that off-shell internal emissions violate the standard NE theorems, requiring a careful treatment beyond the on-shell paradigm, and highlights gravitational Wilson lines as a powerful framework for uncovering deep connections between gauge theories and gravity. Overall, the paper provides a coherent, all-orders-structured view of next-to-soft corrections in high-energy scattering and opens avenues for exploring further power-suppressed effects in both theories and their supergravity extensions.

Abstract

We examine the Regge (high energy) limit of 4-point scattering in both QCD and gravity, using recently developed techniques to systematically compute all corrections up to next-to-leading power in the exchanged momentum i.e. beyond the eikonal approximation. We consider the situation of two scalar particles of arbitrary mass, thus generalising previous calculations in the literature. In QCD, our calculation describes power-suppressed corrections to the Reggeisation of the gluon. In gravity, we confirm a previous conjecture that next-to-soft corrections correspond to two independent deflection angles for the incoming particles. Our calculations in QCD and gravity are consistent with the well-known double copy relating amplitudes in the two theories.

Figures (9)

• Figure 1: Particle labels used throughout for $2\rightarrow2$ scattering.
• Figure 2: The Regge limit as two Wilson lines separated by a transverse distance $\vec{z}$.
• Figure 3: One-loop diagrams entering the calculation of eikonal amplitude ${\cal A}_E$.
• Figure 4: (a) External emisson of a (next-to) soft gluon; (b) Internal emission of a soft gluon.
• Figure 5: External emission contributions from the generalised Wilson line operator of eq. (\ref{['QCDWilsongen']}), where $\bullet$ represents a next-to-soft vertex, and all other vertices are eikonal.