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

Abstract

We present the next-to-next-to-next-to-leading order (N^3LO) 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 N=4 super Yang-Mills theory.

73 pages latex, 14 figures, ancillary Form and Fortran files, final version to appear in JHEP

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Cited by in corpus (3)

• The Collinear Limit of the Energy-Energy Correlator
• Matter dependence of the four-loop QCD cusp anomalous dimension: from small angles to all angles
• Planar master integrals for four-loop form factors