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

Journal of High Energy Physics volume 2017, Article number: 41 (2017) Cite this article

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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  1. II. Institute for Theoretical Physics, Hamburg University, Luruper Chaussee 149, D-22761, Hamburg, Germany

    S. Moch

  2. Nikhef Theory Group, Science Park 105, 1098 XG, Amsterdam, The Netherlands

    B. Ruijl, T. Ueda & J. A. M. Vermaseren

  3. Leiden Centre of Data Science, Leiden University, Niels Bohrweg 1, 2333 CA, Leiden, The Netherlands

    B. Ruijl

  4. Department of Mathematical Sciences, University of Liverpool, Liverpool, L69 3BX, U.K.

    A. Vogt

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  1. S. Moch
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  2. B. Ruijl
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  3. T. Ueda
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  4. J. A. M. Vermaseren
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  5. A. Vogt
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Correspondence to S. Moch.

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ArXiv ePrint: 1707.08315

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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