@**techreport**{RISC7042,author = {J. Ablinger and A. Behring and J. Bluemlein and A. De Freitas and A. von Manteuffel and C. Schneider and K. Schoenwald},

title = {{The non-first-order-factorizable contributions to the three-loop single-mass operator matrix elements $A_{Qg}^{(3)}$ and $Delta A_{Qg}^{(3)}$}},

language = {english},

abstract = {The non-first-order-factorizable contributions to the unpolarized and polarized massive operator
matrix elements to three-loop order, $A_{Qg}^{(3)}$ and $Delta A_{Qg}^{(3)}$, are calculated in the single-mass
case. For the $_2F_1$-related master integrals of the problem, we use a semi-analytic method based
on series expansions and utilize the first-order differential equations for the master integrals which
does not need a special basis of the master integrals. Due to the singularity structure of this basis a part
of the integrals has to be computed to $O(ep^5)$ in the dimensional parameter. The solutions have to be
matched at a series of thresholds and pseudo-thresholds in the region of the Bjorken variable $x in ]0,infty[$
using highly precise series expansions to obtain the imaginary part of the physical amplitude for $x in ]0,1]$
at a high relative accuracy. We compare the present results both with previous analytic results, the results
for fixed Mellin moments, and a prediction in the small-$x$ region. We also derive expansions in
the region of small and large values of $x$. With this paper, all three-loop single-mass unpolarized and
polarized operator matrix elements are calculated.
},

number = {24-02},

year = {2024},

month = {March},

note = {arXiv:2403.00513 [[hep-ph]},

keywords = {Feynman diagram, massive operator matrix elements, computer algebra, differential equations, difference equations, coupled systems, numerics},

length = {14},

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)}

}