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arXiv · 2410.08089

Four-loop splitting functions in QCD -- The gluon-gluon case --

G. Falcioni·F. Herzog·S. Moch·A. Pelloni·A. Vogt
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Abstract

We have computed the even-N moments N =< 20 of the gluon-gluon splitting function P_{gg} at the fourth order of perturbative QCD via the renormalization of off-shell operator matrix elements. Our results, derived analytically for a general compact simple gauge group, agree with all results obtained for this function so far, in particular with the lowest five moments obtained via structure functions in deep-inelastic scattering. Using our new moments and all available endpoint constraints, we construct improved approximations for the four-loop P_{gg}(x) that should be sufficient for a wide range of collider-physics applications. The N^3LO contributions to the scale derivative of the gluon distribution, resulting from these and the corresponding quark-to-gluon splitting functions, amount to 1% or less at x >~ 10^{-4} at a standard reference scale with alpha_s = 0.2.

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G. Falcioni, F. Herzog, S. Moch, A. Pelloni, A. Vogt. 2024-10-10. Four-loop splitting functions in QCD -- The gluon-gluon case --. https://arxiv.org/abs/2410.08089

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