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

We compute the three-loop leading-colour corrections to the Yang-Mills Regge trajectory and gluon impact factor. Conjecturing that, in analogy with 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 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