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

TL;DR

This paper extends cluster-algebraic methods to predict the alphabet of letters for 5- and 6-point QCD processes, revealing new structures and confirming known results in the context of loop amplitudes.

Contribution

It introduces the first candidate letters for 6-point processes with one massive leg and connects cluster algebra predictions to known QCD amplitude alphabets.

Findings

Identified candidate letters for 6-point processes with one massive leg.

Confirmed the alphabet includes all 1-loop integrals for these kinematics.

Discovered 162 potential letters for higher-loop amplitudes.

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.