Some higher moments of deep inelastic structure functions at next-to-next-to leading order of perturbative QCD

TL;DR

This work delivers analytic NNLO (three-loop) QCD results for selected Mellin moments of deep inelastic scattering structure functions in the leading-twist approximation. By applying the operator product expansion and projector techniques within the MINCER/Form framework, the authors compute three-loop anomalous dimensions and coefficient functions for both even (F2, F_L) and odd (F3) moments across multiple N, including singlet and non-singlet sectors. They also address the gamma5 treatment for F3 and perform extensive cross-checks against large-Nf limits and prior results, highlighting computational demands and confirming key sum-rule checks such as the Gross-Llewellyn Smith case. The resulting explicit expressions and numerical values enhance NNLO phenomenology, enable more precise alpha_s determinations, and provide stringent tests for methods aimed at obtaining generic-N three-loop results, while underscoring the need for all-N reconstructions to recover x-dependence.

Abstract

We present the analytic next-to-next-to-leading QCD calculation of some higher moments of deep inelastic structure functions in the leading twist approximation. We give results for the moments $N$=1,3,5,7,9,11,13 of the structure function $F_3$. Similarly we present the moments $N$=10,12 for the flavour singlet and $N$=12,14 for the non-singlet structure functions $F_2$ and $F_L$. We have calculated both the three-loop anomalous dimensions of the corresponding operators and the three-loop coefficient functions of the moments of these structure functions.