The 16th Moment of the Non--Singlet Structure Functions $F_2(x,Q^2)$ and $F_L(x,Q^2)$ to $O(α_s^3)$

TL;DR

This paper computes the 16th Mellin moment of the non--singlet anomalous dimension and the corresponding Wilson coefficients for the structure functions $F_2$ and $F_L$ at three-loop order in pure photon exchange. Using the MINCER framework, it provides an independent cross-check of existing 3-loop results and delivers explicit moment expressions in terms of color factors and flavor numbers. The results, including detailed numerical values and agreement with complete calculations, serve as a stringent validation of high-order QCD calculations and illustrate the substantial computational effort required for such high moments. Overall, the work strengthens confidence in the 3-loop structure of non--singlet DIS and demonstrates the viability of alternative computational approaches for verification.

Abstract

We present the results of an analytic next--to--next--to leading order QCD calculation of the non--singlet anomalous dimension $γ_{\rm NS}^+(N)$ and the coefficient functions $C_{2,L}(N)$ associated to the deeply inelastic structure functions $F_2(x,Q^2)$ and $F_L(x,Q^2)$ for the Mellin moment N=16. Comparisons are made with results in the literature.