The Three-loop splitting functions in QCD: The Singlet case

By A. Vogt, Sven-Olaf Moch, Jos Vermaseren. 2004

1,118 citations recorded by the source corpus.

Abstract We compute the next-to-next-to-leading order (NNLO) contributions to the three splitting functions governing the evolution of unpolarized non-singlet combinations of quark densities in perturbative QCD. Our results agree with all partial results available in the literature. We find that the correct leading logarithmic (LL) predictions for small momentum fractions x do not provide a good estimate of the respective complete results. A new, unpredicted LL contribution is found for the colour factor dabcdabc entering at three loops for the first time. We investigate the size of the corrections and the stability of the NNLO evolution under variation of the renormalization scale. Except for very small x the corrections are found to be rather small even for large values of the strong coupling constant, in principle facilitating a perturbative evolution into the sub-GeV regime.

Subfields: Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/fa6484b4991e4fd363f1265568fbccbf3ef429f2

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Citations in the corpus

The Dilatation Operator of N=4 Super Yang-Mills Theory and Integrability (2004, methodology): “The three-loop QCD result became available after an impressive, full-fledged and rigorous field theoretic computation by Moch, Vermaseren and Vogt [127].”
Integrability and transcendentality (2006, methodology): “ f(g) obeys the Kotikov-Lipatov principle of maximal transcendentality [7], which was actually used in [10] in order to extract, even at ﬁnite spin s, the N = 4 dimensions from the QCD calculation of [9]. When applied to the large slimit, the principle holds that the sum over all the arguments of th”
Four-loop non-singlet splitting functions in the planar limit and beyond (2017, background): “The current precision is at the three-loop level [14, 15] – see refs.”
Antenna subtraction at NNLO with hadronic initial states: initial-final configurations (2009, background): “Moreover, present determinations of parton distribution functions [138–141] at NNLO accuracy [142, 143] can only include data sets for observables where NNLO corrections are known [113, 114, 144–147].”
Factorization at the LHC: From parton distribution functions to initial state jets (2010, background): “[147, 148], and for completeness the result is given in App.”
A Large Hadron Electron Collider at CERN: Report on the Physics and Design Concepts for Machine and Detector (2012, background): “The development of QCD calculations beyond leading order [36, 37] is one of the most remarkable recent achievements of particle physics theory supported by experiment.”
The quark beam function at NNLL (2010, methodology): “ using the two-loop and three-loop αs is numerically very small and well within our theory uncertainties.) Up to three loops, the coeﬃcients of the beta function [46, 47] and cusp anomalous dimension [40, 29] in MS are β0 = 11 3 CA − 4 3 TF nf , β1 = 34 3 C2 A − 20 3 CA +4CF TF nf , β2 = 2857 54 C3”