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arXiv · 1805.09638

On quartic colour factors in splitting functions and the gluon cusp anomalous dimension

S. Moch·B. Ruijl·T. Ueda·J. A. M. Vermaseren·A. Vogt
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Abstract

We have computed the contributions of the quartic Casimir invariants to the four-loop anomalous dimensions of twist-2 spin-N operators at N =< 16. The results provide new information on the structure of the next-to-next-to-next-to-leading order (N^3LO) splitting functions P_{ik}^(3)(x) for the evolution of parton distributions, and facilitate approximate expressions which include the quartic-Casimir contributions to the (light-like) gluon cusp anomalous dimension. These quantities turn out to be closely related, by a generalization of the lower-order `Casimir scaling', to the corresponding quark results. Using these findings, we present an approximate result for the four-loop gluon cusp anomalous dimension in QCD which is sufficient for phenomenological applications.

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S. Moch, B. Ruijl, T. Ueda, J. A. M. Vermaseren, A. Vogt. 2018-05-24. On quartic colour factors in splitting functions and the gluon cusp anomalous dimension. https://doi.org/10.1016/j.physletb.2018.06.017

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