TY  - JOUR
AU  - Ablinger, Jakob
AU  - Behring, A.
AU  - Blümlein, Johannes
AU  - Freitas, Abilio de
AU  - von Manteuffel, A.
AU  - Schneider, Carsten
AU  - Schönwald, K.
TI  - 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> 
JO  - Physics letters / B
VL  - 854
IS  - DESY-24-027
SN  - 0370-2693
CY  - Amsterdam
PB  - North-Holland Publ.
M1  - PUBDB-2024-01880
M1  - DESY-24-027
M1  - arXiv:2403.00513
M1  - RISC Report series 24-02
M1  - ZU-TH 13/24
M1  - CERN-TH-2024-30
M1  - DO-TH 23/15
SP  - 138713
PY  - 2024
AB  - 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.
KW  - master integral (INSPIRE)
KW  - differential equations (INSPIRE)
KW  - factorization (INSPIRE)
KW  - Bjorken (INSPIRE)
KW  - singularity (INSPIRE)
KW  - structure (INSPIRE)
LB  - PUB:(DE-HGF)16
UR  - <Go to ISI:>//WOS:001300809900001
DO  - DOI:10.1016/j.physletb.2024.138713
UR  - https://bib-pubdb1.desy.de/record/607482
ER  -