Four-loop non-singlet splitting functions in the planar limit and beyond



Moch, S, Ruijl, B, Ueda, T, Vermaseren, JAM and Vogt, A
(2017) Four-loop non-singlet splitting functions in the planar limit and beyond. The Journal of High Energy Physics, 2017 (10).

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Abstract

We present the next-to-next-to-next-to-leading order (N3LO) 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 N3LO 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 N=4 super Yang-Mills theory.

Item Type: Article
Uncontrolled Keywords: Perturbative QCD, Resummation
Depositing User: Symplectic Admin
Date Deposited: 11 Oct 2017 11:01
Last Modified: 21 Jan 2022 01:10
DOI: 10.1007/JHEP10(2017)041
Related URLs:
URI: https://livrepository.liverpool.ac.uk/id/eprint/3009918