All-gluon amplitudes with off-shell recursion in multiplet bases

TL;DR

This paper introduces an off-shell recursive method for calculating all-gluon tree-level amplitudes directly in orthogonal multiplet bases, improving computational efficiency for high-multiplicity QCD processes.

Contribution

The work develops a novel recursive framework using Wigner 6j coefficients for efficient all-gluon amplitude computation in orthogonal bases, addressing scalability issues.

Findings

Computational complexity scales as O(17^n) for n-gluon amplitudes.

Algorithm utilizes partial summation and caching for optimization.

Demonstrates potential competitiveness of multiplet bases at high multiplicities.

Abstract

The efficient computation of color-summed QCD amplitudes at high parton multiplicities remains a central challenge for precision collider predictions. Existing approaches using trace, color-flow, or adjoint bases suffer from non-orthogonality, which complicates the color algebra and scales poorly with multiplicity. In this work, we present an off-shell recursive framework for computing all-gluon tree-level amplitudes directly in orthogonal multiplet bases. Utilizing Wigner $6j$ coefficients, we construct an algorithm that builds multiplet-projected off-shell currents from lower-point currents. By optimizing the recursion through partial summation and caching, we find that the computational complexity of calculating $n$-gluon color-summed squared amplitudes scales as $\mathcal{O}(17^n)$. This demonstrates the potential competitiveness of multiplet bases for high-multiplicity processes.