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

A preprint version of the article is available at arXiv.

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 \( \mathcal{N}=4 \) super Yang-Mills theory.

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Moch, S., Ruijl, B., Ueda, T. et al. Four-loop non-singlet splitting functions in the planar limit and beyond. J. High Energ. Phys. 2017, 41 (2017). https://doi.org/10.1007/JHEP10(2017)041

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  • DOI: https://doi.org/10.1007/JHEP10(2017)041

Keywords

  • Perturbative QCD
  • Resummation