The massless three-loop Wilson coefficients for the deep-inelastic structure functions F2, FL, xF3 and g1

Abstract

Abstract We calculate the massless unpolarized Wilson coefficients for deeply inelastic scattering for the structure functions F2(x, Q2), FL(x, Q2), xF3(x, Q2) in the $$ \overline{\textrm{MS}} $$ MS ¯ scheme and the polarized Wilson coefficients of the structure function g1(x, Q2) 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.