The massless three-loop Wilson coefficients for the deep-inelastic structure functions $F_2, F_L, xF_3$ and $g_1$

TL;DR

This paper presents the first calculation of three-loop polarized Wilson coefficients for deep-inelastic scattering, providing new theoretical results and comparisons for unpolarized coefficients, with implications for QCD precision tests.

Contribution

It introduces the first computation of polarized three-loop Wilson coefficients in QCD, using automated methods and Mellin moments, expanding the theoretical understanding of deep-inelastic scattering.

Findings

First polarized three-loop Wilson coefficients calculated.

Comparison with existing unpolarized results confirms accuracy.

Provides small and large x expansions for the coefficients.

Abstract

We calculate the massless unpolarized Wilson coefficients for deeply inelastic scattering for the structure functions $F_2(x,Q^2), F_L(x,Q^2), x F_3(x,Q^2)$ in the $\overline{\sf MS}$ scheme and the polarized Wilson coefficients of the structure function $g_1(x,Q^2)$ in the Larin scheme up to three--loop order in QCD in a fully automated way based on the method of arbitrary high Mellin moments. We work in the Larin scheme in the case of contributing axial--vector couplings or polarized nucleons. For the unpolarized structure functions we compare to results given in the literature. The polarized three--loop Wilson coefficients are calculated for the first time. As a by--product we also obtain the quarkonic three--loop anomalous dimensions from the $O(1/\varepsilon)$ terms of the unrenormalized forward Compton amplitude. Expansions for small and large values of the Bjorken variable $x$ are provided.