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

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

2004-04-14

arxiv.org/abs/hep-ph/0404111v1

Nucl.Phys. B691 (2004) 129-181

Physics

High Energy Physics

High Energy Physics - Phenomenology

41 pages, Latex, 12 figures

Scientific paper

10.1016/j.nuclphysb.2004.04.024

We compute the next-to-next-to-leading order (NNLO) contributions to the splitting functions governing the evolution of the unpolarized flavour-singlet parton densities in perturbative QCD. The exact expressions are presented in both Mellin-N and Bjorken-x space. We also provide accurate parametrizations for practical applications. Our results agree with all partial results available in the literature. As in the non-singlet case, the correct leading logarithmic predictions for small momentum fractions x do not provide good estimates of the respective complete splitting functions. We investigate the size of the corrections and the stability of the NNLO evolution under variation of the renormalization scale. The perturbative expansion appears to converge rapidly at x >~ 10^-3. Relatively large third-order corrections are found at smaller values of x.

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