The massless three-loop Wilson coefficients for the deep-inelastic structure functions F 2 , F L , xF 3 and g 1

Abstract

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), xF 3(x, Q 2) in the MS ¯ $$ \overline{\textrm{MS}} $$ 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/ε) terms of the unrenormalized forward Compton amplitude. Expansions for small and large values of the Bjorken variable x are provided.

Keywords

• Deep Inelastic Scattering or Small-x Physics
• Higher-Order Perturbative Calculations
• Renormalization Group
• The Strong Coupling