%0 Journal Article
%A Ablinger, Jakob
%A Behring, A.
%A Blümlein, Johannes
%A Freitas, Abilio de
%A von Manteuffel, A.
%A Schneider, Carsten
%A Schönwald, K.
%T The non-first-order-factorizable contributions to the three-loop single-mass operator matrix elements A<sub>Qg</sub><sup>(3)</sup> and ∆A<sub>Qg</sub><sup>(3)</sup> 
%J Physics letters / B
%V 854
%N DESY-24-027
%@ 0370-2693
%C Amsterdam
%I North-Holland Publ.
%M PUBDB-2024-01880
%M DESY-24-027
%M arXiv:2403.00513
%M RISC Report series 24-02
%M ZU-TH 13/24
%M CERN-TH-2024-30
%M DO-TH 23/15
%P 138713
%D 2024
%X The non-first-order-factorizable contributions (The terms 'first-order-factorizable contributions' and 'non-first-order-factorizable contributions' have been introduced and discussed in Refs. . They describe the factorization behaviour of the difference- or differential equations for a subset of master integrals of a given problem.) to the unpolarized and polarized massive operator matrix elements to three-loop order, A<sub>Qg</sub><sup>(3)</sup> and ∆A<sub>Qg</sub><sup>(3)</sup>, are calculated in the single-mass case. For the <sub>2</sub>F<sub>1</sub>-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(ε<sup>5</sup>) 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  ∈ ]0,∞[ using highly precise series expansions to obtain the imaginary part of the physical amplitude for x  ∈ ]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.
%K master integral (INSPIRE)
%K differential equations (INSPIRE)
%K factorization (INSPIRE)
%K Bjorken (INSPIRE)
%K singularity (INSPIRE)
%K structure (INSPIRE)
%F PUB:(DE-HGF)16
%9 Journal Article
%U <Go to ISI:>//WOS:001300809900001
%R 10.1016/j.physletb.2024.138713
%U https://bib-pubdb1.desy.de/record/607482