Five-loop contributions to low-N non-singlet anomalous dimensions in QCD

We present the first calculations of next-to-next-to-next-to-next-to-leading order (N$^4$ LO) contributions to anomalous dimensions of spin- N twist-2 operators in perturbative QCD. Specifically, we have obtained the respective non-singlet quark–quark anomalous dimensions at $N = 2$ and $N = 3$ to the fifth order in the strong coupling $α_s$ . These results set the scale for the N$^4$LO contributions to the evolution of the non-singlet quark distributions of hadrons outside the small-$x$ region, and facilitate a first approximate determination of the five-loop cusp anomalous dimension. While the N$^4$LO coefficients are larger than expected from the lower-order results, their inclusion stabilizes the perturbative expansions for three or more light flavours at a sub-percent accuracy for $α_s <$ 0.3