Low moments of the four-loop splitting functions in QCD

Moch, Sven-Olaf; Ueda, Takahiro; Vogt, Andreas; Ruijl, Ben; Vermaseren, Jos

Preprint

PUBDB-2021-04837

Low moments of the four-loop splitting functions in QCD

Moch, S.-O. (Corresponding author)Extern* ; Ruijl, B. ; Ueda, T. ; Vogt, A. ; Vermaseren, J.

This record in other databases:

Report No.: DESY-21-203; LTH 1282; NIKHEF 21-030; arXiv:2111.15561

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 $x \gtrsim 0.1$, 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 $\alpha_s \lesssim 0.2$. 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.

Keyword(s): strong interaction: coupling constant ; parton: density ; evolution equation ; DGLAP equation ; splitting function ; operator product expansion ; quantum chromodynamics ; quark ; gluon ; perturbation theory ; higher-order: 4 ; Mellin transformation