The massless three-loop Wilson coefficients for the deep-inelastic structure functions $F_2,F_L,x{F}_3$ and $g_1$

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 $\overline{\mathsf{MS}}$ 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 $O(1/\epsilon )$ terms of the unrenormalized forward Compton amplitude. Expansions for small and large values of the Bjorken variable $x$ are provided.

159 pages Latex