Real next-to-leading corrections to the multigluon amplitudes in the helicity formalism

TL;DR

This work computes real next-to-leading corrections to tree-level multigluon amplitudes in the high-energy MRK using the helicity formalism. It demonstrates that forward- and central-rapidity real corrections, obtained via Parke-Taylor amplitudes, are equivalent to the corresponding Fadin-Lipatov amplitudes for fixed helicities, with a simpler algebraic structure than in the general FL expressions. The results reinforce the consistency of MRK-based BFKL building blocks and provide a framework for evaluating real NLL corrections to the BFKL kernel, while outlining future extensions to quark-antiquark production. Overall, the paper strengthens the helicity-based approach as a practical tool for high-energy QCD amplitudes and their resummation properties.

Abstract

Using the helicity formalism, we compute the corrections to the tree-level multigluon amplitudes in the high-energy limit, induced by the corrections to the multi-Regge kinematics, and we show that they coincide with the corresponding Fadin-Lipatov amplitudes at fixed helicities.

Figures (10)

• Figure 1: Multigluon amplitude in multiregge kinematics at the tree level. The blobs remind that non-local effective Lipatov vertices are used for the gluon emissions along the ladder.
• 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 lego plot.
• Figure 3: Leading helicity configurations of the 3-gluon production amplitude, with 2 negative-helicity gluons. The gluons are labelled by their momenta, always taken as outgoing, their colors and helicities. Gluons $k_1$ and $k_2$ are produced in the forward-rapidity region of gluon $k_0$.
• Figure 4: 3-gluon production amplitude in the color ordering ($a$) [$0,1,2,p',p$] and ($b$) ($1\leftrightarrow 2$).
• Figure 5: 3-gluon production amplitude in the color ordering ($a$) [$0,1,2,p,p'$] and ($b$) ($1\leftrightarrow 2$); ($c$) [$0,1,p',p,2$] and ($d$) ($1\leftrightarrow 2$).