The 3-loop QCD calculation of the moments of deep inelastic structure functions

TL;DR

This work delivers the analytic three-loop QCD corrections necessary for NNLO (NNL) predictions of deep inelastic scattering structure-function moments, providing singlet and non-singlet anomalous dimensions and coefficient functions for N=2,4,6,8 (and N=10 non-singlet). The authors employ an OPE-based formalism, dimensional regularization, and a projection method to reduce to propagator-type diagrams, using automated tools to manage the computational complexity. The resulting expressions illuminate the impact of 3-loop effects on $F_2$ and $F_L$ evolution and enable reconstruction of x-space distributions, with consistency checks against known limits and partial high-$n_f$ results. While fully determining all higher moments remains challenging due to computational demands, the paper demonstrates stable, analytic results for the key low-to-moderate moments and discusses their phenomenological implications for DIS analyses.

Abstract

We present the analytic next-to-next-to-leading perturbative QCD corrections in the leading twist approximation for the moments N=2,4,6,8 of the flavour singlet deep inelastic structure functions F_2 and F_L. We calculate the three-loop anomalous dimensions of the corresponding singlet operators and the three-loop coefficient functions of the structure functions F_L and F_2. In addition, we obtained the 10th moment for the non-singlet structure functions in the same order of perturbative QCD. We perform an analysis of the obtained results.