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

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 \( \mathcal{O}\left({17}^n\right) \). This demonstrates the potential competitiveness of multiplet bases for high-multiplicity processes.