# Two-parton scattering in the high-energy limit

## TL;DR

This paper advances the understanding of high-energy gauge-theory scattering by computing three-loop Regge-cut contributions, revealing new mixing effects between Reggeized gluon states, and enabling predictions of high-energy logarithms at higher loops.

## Contribution

It introduces a novel formalism using the Balitsky-JIMWLK equation to compute NNLL Regge-cut contributions and uncovers mixing effects between different Reggeized gluon states at three loops.

## Key findings

- Computed three-loop Regge-cut contributions in the high-energy limit.
- Discovered mixing between states with different numbers of Reggeized gluons at NNLL.
- Extracted the three-loop Regge trajectory in ${\

## Abstract

Considering $2\to 2$ gauge-theory scattering with general colour in the high-energy limit, we compute the Regge-cut contribution to three loops through next-to-next-to-leading high-energy logarithms (NNLL) in the signature-odd sector. Our formalism is based on using the non-linear Balitsky-JIMWLK rapidity evolution equation to derive an effective Hamiltonian acting on states with a fixed number of Reggeized gluons. A new effect occurring first at NNLL is mixing between states with $k$ and $k+2$ Reggeized gluons due non-diagonal terms in this Hamiltonian. Our results are consistent with a recent determination of the infrared structure of scattering amplitudes at three loops, as well as a computation of $2\to 2$ gluon scattering in ${\cal N}=4$ super Yang-Mills theory. Combining the latter with our Regge-cut calculation we extract the three-loop Regge trajectory in this theory. Our results open the way to predict high-energy logarithms through NNLL at higher-loop orders.