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<p>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<i>j</i> 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 <i>n</i>-gluon color-summed squared amplitudes scales as <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="13130_2025_27460_Article_IEq1.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="54" /> </InlineMediaObject> <EquationSource Format="MATHML"><math display="inline"> <mi mathvariant="script">O</mi> <mfenced close=")" open="("> <msup> <mn>17</mn> <mi>n</mi> </msup> </mfenced> </math></EquationSource> <EquationSource Format="TEX">\( \mathcal{O}\left({17}^n\right) \)</EquationSource> </InlineEquation>. This demonstrates the potential competitiveness of multiplet bases for high-multiplicity processes.</p>

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

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年10月21日

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  • Oskar Bolinder,
  • Rikkert Frederix,
  • Malin Sjodahl

摘要

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