The Three-Loop Splitting Functions in QCD: The Non-Singlet Case

Details The Three-Loop Splitting Functions in QCD: The Non-Singlet Case The Three-Loop Splitting Functions in QCD: The Non-Singlet Case

2004-03-17

arxiv.org/abs/hep-ph/0403192v1

Nucl.Phys.B688:101-134,2004

Physics

High Energy Physics

High Energy Physics - Phenomenology

29 pages, Latex, 9 figures

Scientific paper

10.1016/j.nuclphysb.2004.03.030

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 d^{abc}d_{abc} 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.

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