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 Nc-subleading terms are absent from the three-loop Regge trajectory, we understand our result as the first computation of the pure gauge, or nf = 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.
Highlights
Conjecturing that, in analogy with N = 4 super YangMills (SYM), in a suitable scheme Nc-subleading terms are absent from the three-loop Regge trajectory, we understand our result as the first computation of the pure gauge, or nf = 0, part of the QCD three-loop Regge trajectory
As it is apparent from the colour coefficient (F a3)a2c(F a4)a1c, in eq (1.1) only the antisymmetric octet 8a is exchanged in the t channel
Regge-cut scheme Nc-subleading terms are absent from the three-loop Regge trajectory in N = 4 SYM
Summary
In ref. [48], the planar SU(Nc) Yang-Mills gg → gg amplitude was computed through three loops in all helicity configurations. Since our goal is to extract the building blocks appearing in the high-energy factorisation given in eq (1.5), we need to project the full amplitude onto the antisymmetric octet channel. This can be achieved by contracting it with the colour projector,. We normalise by the tree-level amplitude M[+8+a]−(0−) as in eq (1.10), and compute the BFKL building blocks by extracting them from the real part of the colour-ordered amplitude M++−− given in [48]. As detailed, the building blocks we extract from this computation match established results which were computed in the HV scheme, in which the external gluons are restricted to four dimensions and to two polarisation states
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