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

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.

11 pages, LaTeX, 2 figures. FORM file of the main results available with the source. v2: Nikhef and DESY numbers added, one very minor text modification. Version to appear in Phys. Lett. B

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• Riemann $\zeta (4)$ function contributions to $O\left({{\alpha }_s}^5\right)$ terms of Adler D-function and Bjorken polarized sum rule in $SU\left(N_c\right)$ QCD: results and consequences