The gluon Regge trajectory at three loops from planar Yang-Mills theory

TL;DR

This paper calculates the three-loop gluon Regge trajectory in planar Yang-Mills theory, providing new insights into high-order corrections relevant for quantum chromodynamics and BFKL theory.

Contribution

It presents the first pure gauge, three-loop Regge trajectory calculation in QCD, extending previous results and aligning with predictions from infrared factorisation and $ ext{N}=4$ SYM.

Findings

Results are consistent with infrared factorisation predictions.

Reproduces known $ ext{N}=4$ SYM results with maximal weight truncation.

Includes dependence on a Regge factorisation scale for future BFKL applications.

Abstract

We compute the three-loop leading-colour corrections to the Yang-Mills Regge trajectory and gluon impact factor. Conjecturing that, in analogy with $\mathcal{N}=4$ super Yang-Mills (SYM), in a suitable scheme $N_c$-subleading terms are absent from the three-loop Regge trajectory, we understand our result as the first computation of the pure gauge, or $n_f = 0$, part of the QCD three-loop Regge trajectory. The results are presented both for the bare and renormalised amplitudes and are consistent with predictions from infrared factorisation along with reproducing known results in planar $\mathcal{N}=4$ SYM through a maximal weight truncation. We also include the dependence on a Regge factorisation scale to facilitate future applications in BFKL theory at next-to-next-to leading logarithmic accuracy.