Equivalence of the Parke-Taylor and the Fadin-Kuraev-Lipatov amplitudes in the high-energy limit

TL;DR

The article addresses the high-energy behavior of tree-level multigluon amplitudes by unifying Parke-Taylor and FKL descriptions through color flows ordered by rapidity on a two-sided plot. It demonstrates that, for helicity configurations common to both formalisms, the PT and FKL amplitudes are identical, with leading-color configurations aligning with the rapidity ordering. The analysis leverages spinor-helicity techniques in multiregge kinematics and reveals that the ladder structure and color flow persist under leading-log loop corrections. This provides a cohesive framework for understanding multi-jet processes in the MRK regime and supports interchangeable use of PT and FKL results for the dominant configurations.

Abstract

We give a unified description of tree-level multigluon amplitudes in the high-energy limit. We represent the Parke-Taylor amplitudes and the Fadin-Kuraev-Lipatov amplitudes in terms of color configurations that are ordered in rapidity on a two-sided plot. We show that for the helicity configurations they have in common the Parke-Taylor amplitudes and the Fadin-Kuraev-Lipatov amplitudes coincide.

Figures (4)

• Figure 1: PT amplitude with color ordering [$A,0,...,n+1,B$].
• Figure 2: $a)$ PT amplitude with color ordering [$A,0,...,j-1,j+1,...,n+1,B, j$], and $b)$ its untwisted version on the two-sided plot.
• Figure 3: $a)$ PT amplitude with color ordering [$A,0,...,j-1,j+1,...,k-1, k+1,...,n+1,B,k,j$], and $b)$ its untwisted version on the two-sided plot.
• Figure 4: FKL amplitude for fixed gluon helicities. The blobs remind that Lipatov vertices are used for the gluon emissions along the ladder.