Computer Algebra for Multi-Loop Feynman Integrals

Project Lead

Project Duration

01/09/2021 - 31/08/2025




The Two-Loop Massless Off-Shell QCD Operator Matrix Elements to Finite Terms

J. Blümlein, P. Marquard, C. Schneider, K. Schönwald

To appear in Nuclear Physics B(22-01), pp. ?-?. February 2022. ISSN 0550-3213. arXiv:2202.03216 [hep-ph]. [doi]
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 upto 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. },
journal = {To appear in Nuclear Physics B},
number = {22-01},
pages = {?--?},
isbn_issn = {ISSN 0550-3213},
year = {2022},
month = {February},
note = {arXiv:2202.03216 [hep-ph]},
refereed = {yes},
keywords = {QCD, Operator Matrix Element, 2-loop Feynman diagrams, computer algebra, large moment method},
length = {0},
url = {}