| Article | |
| Report number | arXiv:2403.00513 ; ZU-TH-13/24 ; DO-TH-23/15 ; RISC Report series 24-02 ; CERN-TH-2024-30 ; DESY-24-027 |
| Title | The non-first-order-factorizable contributions to the three-loop single-mass operator matrix elements and |
| Related title | The non-first-order-factorizable contributions to the three-loop single-mass operator matrix elements $A_{Qg}^{(3)}$ and $\Delta A_{Qg}^{(3)}$ |
| Author(s) | Ablinger, J. (Linz U. ; Linz U., RISC ; OAW, Linz, RICAM) ; Behring, A. (CERN) ; Blümlein, J. (DESY, Zeuthen ; Dortmund U.) ; De Freitas, A. (Linz U. ; Linz U., RISC ; DESY, Zeuthen) ; von Manteuffel, A. (Regensburg U.) ; Schneider, C. (Linz U. ; Linz U., RISC) ; Schönwald, K. (Zurich U.) |
| Publication | 2024-05-13 |
| Imprint | 2024-03-01 |
| Number of pages | 8 |
| In: | Phys. Lett. B 854 (2024) pp.138713 |
| DOI | 10.1016/j.physletb.2024.138713 (publication) 10.1016/j.physletb.2024.138713 (publication) |
| Subject category | hep-ph ; Particle Physics - Phenomenology |
| Abstract | 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. \cite{Behring:2023rlq,Ablinger:2023ahe}. 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, $A_{Qg}^{(3)}$ 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 $O(\varepsilon^5)$ 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. |
| Copyright/License | preprint: (License: CC BY 4.0) publication: © 2024 The Author(s) (License: CC BY 4.0) |
Corresponding record in: Inspire
Δημιουργία εγγραφής 2024-06-12, τελευταία τροποποίηση 2024-09-19