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arXiv · 2507.22636

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

Oskar Bolinder·Rikkert Frederix·Malin Sjodahl
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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.

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Oskar Bolinder, Rikkert Frederix, Malin Sjodahl. 2025-07-30. All-gluon amplitudes with off-shell recursion in multiplet bases. https://arxiv.org/abs/2507.22636

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