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

## TL;DR

This paper calculates the five-loop contributions to non-singlet anomalous dimensions in QCD, providing crucial data for high-precision evolution of quark distributions and advancing the understanding of perturbative QCD at N^4LO.

## Contribution

It presents the first N^4LO calculations of non-singlet anomalous dimensions at N=2 and 3 in QCD, extending perturbative accuracy to five loops.

## Key findings

- N^4LO coefficients are larger than lower-order predictions.
- Including N^4LO stabilizes perturbative expansions for alpha_s < 0.3.
- Results enable more precise evolution of non-singlet quark distributions.

## Abstract

We present the first calculations of next-to-next-to-next-to-next-to-leading order (N^4LO) 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 alpha_s. These results set the scale for the N^4LO 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^4LO 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 alpha_s < 0.3.