On the computation of multigluon amplitudes

TL;DR

This paper introduces a recursive-equation framework to compute multigluon amplitudes at high-energy colliders, addressing the factorial growth of traditional Feynman approaches. By employing a generating-function formalism and recasting colour and helicity sums as Monte Carlo integrations, the authors achieve a computational cost that scales as approximately $3^n$, enabling precise tree-level calculations for $gg\to(n-2)g$ up to nine gluons. Key contributions include a nonlinear recursion for momentum-partition coefficients, color-flow reformulations that diagonalize three-gluon interactions, and a systematic treatment of helicity sums via a phase integration. The results demonstrate feasibility and efficiency, with cross sections and differential distributions aligning qualitatively with SPHEL and highlighting the method's potential as an exact tree-level multi-jet event generator for the LHC.

Abstract

A computational algorithm based on recursive equations is developed in order to estimate multigluon production processes at high energy hadron colliders. The partonic reactions gg->(n-2)g with n up to n=9 are studied and comparisons with known approximations are presented.

Figures (2)

• Figure 1: Differential distributions for the process $gg\to 6g$ in pb/GeV; (a) maximum transverse momentum, (b) minimum transverse momentum, (c) maximum two-jet invariant mass and (d) minimum two-jet invariant mass. Black circles correspond to the exact result whereas triangles represent the predictions of SPHEL.
• Figure 2: Same as Fig.\ref{['fig1']} for $gg\to 7g$.