Double spacelike collinear limits from multi-Regge kinematics

TL;DR

This paper investigates the double spacelike collinear limits in planar $ ext{N}=4$ Super Yang-Mills theory, revealing a universal generalized splitting amplitude that connects collinear factorization with multi-Regge kinematics and integrability.

Contribution

It introduces a generalized splitting amplitude for double spacelike collinear limits, confirming recent proposals and demonstrating its universality across various scattering processes.

Findings

The generalized splitting amplitude matches the BDS subtracted six-point amplitude in multi-Regge kinematics.

The amplitude can be explicitly evaluated using integrability to all orders.

Evidence shows the universality of the splitting amplitude across different particle numbers and loop orders.

Abstract

We study scattering amplitudes and form factors in planar $\mathcal{N}=4$ Super Yang-Mills theory in the limit where two pairs of gluons become collinear. We find that, when the virtualities of both collinear pairs are spacelike, the collinear factorisation of the amplitude involves a generalised splitting amplitude that correlates the two collinear directions, confirming a recent proposal in the literature. Remarkably, we find that our generalised splitting amplitude agrees with the Bern-Dixon-Smirnov (BDS) subtracted six-point amplitude in multi-Regge kinematics. The latter can be explicitly evaluated using integrability to all orders in the coupling. We also present compelling evidence for the universality of the generalised splitting amplitude, by showing that the same function governs the double spacelike collinear limit of scattering amplitudes with up to 8 particles and 3 loops and form factors with up to 6 particles and 2 loops.