The high energy limit of QCD at two loops

TL;DR

The paper tests the high-energy (Regge) limit of two-loop QCD amplitudes for parton scattering by revisiting the reggeized-gluon exchange framework (BFKL). It confirms the LL and NLL predictions and re-derives the two-loop Regge trajectory in agreement with established results, while uncovering a breakdown of universality at NNLL due to potential three-reggeized-gluon exchanges. The analysis relies on the interference with tree amplitudes and highlights the need for amplitude-level checks to fully capture all color structures. Overall, it strengthens the understanding of Reggeization in QCD up to two loops and points to new dynamics beyond the standard BFKL ansatz at NNLL.

Abstract

By taking the high-energy limit of the two-loop amplitudes for parton-parton scattering, we have tested the validity of Fadin-Lipatov's ansatz for parton-parton scattering in the high-energy limit. As expected, we have found that it holds at LL and NLL accuracy, and hence we have independently re-evaluated the two-loop Regge trajectory, finding full agreement with the previous results by Fadin and collaborators. We have found, though, that the universality implied by the ansatz is violated at the next-to-next-to-leading logarithmic level.

Figures (3)

• Figure 1: The symbolic representation of the factorised form for the high energy limit of the parton-parton scattering amplitude. The blobs represent the coefficient functions $C^{i}(p_a,p_{a'})$ (for $i=g,~q$) while the zigzag line describes the reggeized gluon exchange.
• Figure 2: Schematic one-loop expansion of the factorised form for the high energy limit of the parton-parton scattering amplitude. The pairs of concentric circles represent the one-loop corrections to the impact factor and regge trajectory and the individual diagrams represent terms that contribute at (a) leading and (b) next-to-leading logarithmic order.
• Figure 3: Schematic two-loop expansion of the factorised form for the high energy limit of the parton-parton scattering amplitude. The combinations of ovals and circles represent the one-loop and two-loop corrections to the impact factor and regge trajectory and the individual diagrams represent terms that contribute at (a) leading, (b) next-to-leading and (c) next-to-next-to-leading logarithmic order.