Next-to-Leading Corrections to the BFKL Equation

TL;DR

This work utilizes the helicity formalism in the high-energy limit to derive real next-to-leading-logarithmic corrections to the BFKL equation. It constructs the full set of real-emission amplitudes in both forward- and central-rapidity regions, identifying the emission vertices (including g*g->gg, g*g->qqbar, and Lipatov-type ladder emissions) that feed the NLL BFKL kernel. By detailing explicit tree-level and near-NLL amplitudes, the paper provides building blocks and boundary conditions necessary for a complete NLL resummation in small-x processes such as DIS and high-energy hadron collisions. The results advance the practical implementation of NLL BFKL corrections and deepen the understanding of high-energy QCD dynamics.

Abstract

Using the helicity formalism in the high-energy limit, we compute the amplitudes which generate the real next-to-leading-logarithmic corrections to the BFKL equation. Accordingly, we provide a list of all the off-shell vertices necessary to build such amplitudes.

Figures (4)

• Figure 1: $(a)$ Amplitude for $g\, g \rightarrow g\, g$ scattering and $(b),\,(c)$ for $q\, g \rightarrow q\, g$ scattering. We label the external lines with momentum, always taken as outgoing, color and helicity, and the internal lines with momentum and color.
• Figure 2: $(a)$ Amplitude for $g\, g \rightarrow g\, g\, g$ scattering, and $(b)$ for the production of $n+2$ gluons.
• Figure 3: Amplitudes for the production of three partons, with partons $k_1$ and $k_2$ in the forward-rapidity region of parton $k_0$.
• Figure 4: Amplitudes for the production of four partons, with partons $k_1$ and $k_2$ in the central-rapidity region.