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

A bstract 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 6 j 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 $$ \mathcal{O}\left({17}^n\right) $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>O</mml:mi> <mml:mfenced> <mml:msup> <mml:mn>17</mml:mn> <mml:mi>n</mml:mi> </mml:msup> </mml:mfenced> </mml:math> . This demonstrates the potential competitiveness of multiplet bases for high-multiplicity processes.