@**techreport**{RISC6487,author = {J. Blümlein and P. Marquard and C. Schneider and K. Schönwald},

title = {{The Two-Loop Massless Off-Shell QCD Operator Matrix Elements to Finite Terms}},

language = {english},

abstract = {We calculate the unpolarized and polarized two--loop massless off--shell operator matrix elements in QCD
to $O(ep)$ in the dimensional parameter in an automated way. Here we use the method of arbitrary high
Mellin moments and difference ring theory, based on integration-by-parts relations. This method also
constitutes one way to compute the QCD anomalous dimensions. The presented higher order contributions to
these operator matrix elements occur as building blocks in the corresponding higher order calculations up
to four--loop order. All contributing quantities can be expressed in terms of harmonic sums in Mellin--$N$
space or by harmonic polylogarithms in $z$--space. We also perform comparisons to the literature. },

number = {22-01},

year = {2022},

month = {February},

keywords = {QCD, Operator Matrix Element, 2-loop Feynman diagrams, computer algebra, large moment method},

length = {101},

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)}

}