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arXiv · 2603.16743

Novel cluster-algebraic letters for 5- and 6-point QCD processes

Rigers Aliaj·Gabriele Dian·Georgios Papathanasiou
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Abstract

By breaking dual conformal invariance, we transform cluster-algebraic predictions for the alphabet of 9-point amplitudes in $\mathcal{N}=4$ super Yang-Mills theory to analogous predictions for 5- and 6-point processes in QCD. We start by obtaining, for the first time, candidate letters for 6-point processes with one massive external leg, and discover that they surprisingly also contain nested square roots. We confirm that our results essentially contain the alphabet of all 1-loop integrals with these kinematics, and in their massless limit also the recently computed alphabet of finite, planar 2-loop amplitudes for 6-point massless QCD processes. In the latter case, we additionally find 162 letters that may appear at higher loops. We similarly produce candidate letters for 5-point 2-mass processes, whose comparison with the literature reveals a nontrivial overlap that also includes new letters.

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Rigers Aliaj, Gabriele Dian, Georgios Papathanasiou. 2026-03-17. Novel cluster-algebraic letters for 5- and 6-point QCD processes. https://arxiv.org/abs/2603.16743

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