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arXiv · 2111.15561

Low moments of the four-loop splitting functions in QCD

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

We have computed the four lowest even-N moments of all four splitting functions for the evolution of flavour-singlet parton densities of hadrons at the fourth order in the strong coupling constant alpha_s. The perturbative expansion of these moments, and hence of the splitting functions for momentum fractions x >~ 0.1, is found to be well behaved with relative alpha_s-coefficients of order one and sub-percent effects on the scale derivatives of the quark and gluon distributions at alpha_s ~< 0.2. More intricate computations, including other approaches such as the operator-product expansion, are required to cover the full x-range relevant to LHC analyses. Our results are presented analytically for a general gauge group for detailed checks and validations of such future calculations.

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S. Moch, B. Ruijl, T. Ueda, J. A. M. Vermaseren, A. Vogt. 2021-11-30. Low moments of the four-loop splitting functions in QCD. https://doi.org/10.1016/j.physletb.2021.136853

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