Analysis of the anomalous-dimension matrix of n-jet operators at 4 loops

Recently, an all-order conjecture for the anomalous-dimension matrix of n-jet operators in SCET was proposed, which allows one to predict the structure of the infrared divergences of dimensionally regularized, massless gauge-theory scattering amplitudes with an arbitrary number of legs and loops. The conjecture is severely constrained by soft-collinear factorization, non-abelian exponentiation, and the behavior of amplitudes in collinear limits. Using these constraints, a diagrammatic analysis has shown that the anomalous dimension involves only two-parton correlators up to three loop order. The only exception is given by a single color structure multiplying a function of conformal cross ratios depending on the momenta of four external partons, which would have to vanish in all two-particle collinear limits. We extend this analysis by completing the diagrammatic analysis at four loop, and we find that additional functions which vanish in all two-particle collinear limits may arise.