When does the gluon reggeize?

TL;DR

This paper uses the eikonal approximation to analyze gluon reggeization in high-energy processes, revealing new insights into BFKL dynamics and proposing a Wilson line-based approach that avoids the concept of reggeized gluons.

Contribution

It introduces a Wilson line framework for high-energy QCD processes that bypasses the traditional reggeized gluon concept, supported by exact computations in N=4 super Yang-Mills.

Findings

Gluon reggeization can be understood via the eikonal approach.

Starting from four loops, BFKL dynamics conflict with certain infrared divergence conjectures.

In N=4 SYM, reggeized gluons appear as resonances with width proportional to coupling.

Abstract

We propose the eikonal approximation as a simple and reliable tool to analyze relativistic high-energy processes, provided that the necessary subtleties are accounted for. An important subtlety is the need to include eikonal phases for a rapidity-dependent collection of particles, as embodied by the Balitsky-JIMWLK rapidity evolution equation. In the first part of this paper, we review how the phenomenon of gluon reggeization and the BFKL equations can be understood simply (but not too simply) in the eikonal approach. We also work out some previously overlooked implications of BFKL dynamics, including the observation that starting from four loops it is incompatible with a recent conjecture regarding the structure of infrared divergences. In the second part of this paper, we propose that in the strict planar limit the theory can be developed to all orders in the coupling with no reference at all to the concept of "reggeized gluon." Rather, one can work directly with a finite, process-dependent, number of Wilson lines. We demonstrate consistency of this proposal by an exact computation in N=4 super Yang-Mills, which shows that in processes mediated with two Wilson lines the reggeized gluon appears in the weak coupling limit as a resonance whose width is proportional to the coupling. We also provide a precise operator definition of Lipatov's integrable spin chain, which is manifestly integrable at any value of the coupling as a result of the duality between scattering amplitudes and Wilson loops in this theory.