Four-Loop Non-Singlet Splitting Functions in the Planar Limit and Beyond

Moch, S.; Ueda, T.; Vogt, A.; Vermaseren, J. A. M.; Ruijl, B.

Preprint/Report

PUBDB-2017-10329

Four-Loop Non-Singlet Splitting Functions in the Planar Limit and Beyond

Moch, S. (Corresponding author)Extern* ; Ruijl, B. ; Ueda, T. ; Vermaseren, J. A. M. ; Vogt, A.

2017

[10.3204/PUBDB-2017-10329]

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Please use a persistent id in citations: doi:10.3204/PUBDB-2017-10329

Report No.: DESY-17-106; LTH-1139; NIKHEF-2017-034; arXiv:1707.08315

Abstract: We present the next-to-next-to-next-to-leading order (N$^3$LO) contributions to the non-singlet splitting functions for both parton distribution and fragmentation functions in perturbative QCD. The exact expressions are derived for the terms contributing in the limit of a large number of colours. For the remaining contributions, approximations are provided that are sufficient for all collider-physics applications. From their threshold limits we derive analytical and high-accuracy numerical results, respectively, for all contributions to the four-loop cusp anomalous dimension for quarks, including the terms proportional to quartic Casimir operators. We briefly illustrate the numerical size of the four-loop corrections, and the remarkable renormalization-scale stability of the N^3LO results, for the evolution of the non-singlet parton distribution and the fragmentation functions. Our results appear to provide a first point of contact of four-loop QCD calculations and the so-called wrapping corrections to anomalous dimensions in $\mathcal{N}$=4 super Yangs-Mills theory.

Keyword(s): parton: distribution function ; supersymmetry: 4 ; quantum chromodynamics: perturbation theory ; fragmentation function ; anomalous dimension ; splitting function ; higher-order: 3 ; expansion 1/N: color ; numerical calculations