@**techreport**{RISC6583,author = {J. Blümlein and P. Marquard and C. Schneider and K. Schönwald},

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

language = {english},

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 $O(1/ep)$ terms of the unrenormalized forward Compton amplitude.
Expansions for small and large values of the Bjorken variable $x$ are provided.
},

number = {22-12},

year = {2022},

month = {August},

note = {arXiv:2208.14325 [hep-ph]},

keywords = {massless unpolarized Wilson coefficients, large moment method, linear difference equations, computer algebra,coupled systems of linear differential equations},

length = {160},

license = {CC BY 4.0 International},

type = {RISC Report Series},

institution = {Research Institute for Symbolic Computation (RISC), Johannes Kepler University Linz},

address = {Altenberger Straße 69, 4040 Linz, Austria},

issn = {2791-4267 (online)}

}