Quark-antiquark contribution to the multigluon amplitudes in the helicity formalism

TL;DR

This work uses the helicity formalism to compute the quark–antiquark contribution to tree-level multigluon amplitudes in the high-energy limit, focusing on forward- and central-rapidity regions relevant to real NLx corrections of the BFKL kernel. By deriving explicit amplitudes for $g g o g ar{q}q$ and $g g o g ar{q}q g$, and relating them to purely gluonic amplitudes via N=1 SUSY Ward identities, the paper provides the necessary vertices and color structures to complete the real NLx corrections and to connect to the gluon anomalous dimension at small $x$. Key results include forward-rapidity vertices $C^{gar{q}q}$ and central-rapidity vertices $A^{ar{q}q}_{- u u}$, with careful attention to helicity configurations, collinear limits, and multi-Regge behavior. These contributions set the stage for incorporating virtual NLx corrections through known one-loop multiparton helicity amplitudes and thus advance precise high-energy QCD predictions.

Abstract

Using the helicity formalism, we compute the contribution of a quark-antiquark pair to the tree-level multigluon amplitudes in the high-energy limit. The $\bar{q}\, q$-pair production is absent in the leading-log formalism, but contributes to the next-to-leading corrections to it, and is therefore relevant for the computation of parton-parton scattering in the high-energy limit and of the gluon anomalous dimension at small $x_{bj}$, at next-to-leading accuracy.

Figures (5)

• Figure 1: 3-gluon production amplitude. 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 2: Amplitude for the scattering $g\, g \rightarrow g\, \bar{q}\, q$, with $k_1$ the antiquark. The $\bar{q}\, q$ pair is produced in the forward-rapidity region of gluon $k_0$.
• Figure 3: Amplitude for the scattering $g\, g \rightarrow g\, \bar{q}\, q\, g$. with $k_1$ the antiquark. The $\bar{q}\, q$ pair is produced in the central-rapidity region.
• Figure 4: Amplitude for the scattering $g\, g \rightarrow 4 g$, with two gluon produced in the central-rapidity region.
• Figure 5: The supersymmetric Ward identity relating the amplitude $g\, g \rightarrow 4\, g$ to the amplitudes $g\, g \rightarrow g\, \bar{q}\, q\, g$ and $f\, g \rightarrow g\, f\, g\, g$, with $f = \bar{q}, q$.