Ablinger, J. and Behring, A. and Bluemlein, J. and De Freitas, A. and von Manteuffel, A. and Schneider, C. and Schoenwald, K. (2024) The first-order factorizable contributions to the three-loop massive operator matrix elements A<SUP>(3)</SUP>Qg and ΔA<SUP>(3)</SUP>Qg. NUCLEAR PHYSICS B, 999: 116427. -. ISSN 0550-3213, 1873-1562
Full text not available from this repository.Abstract
The unpolarized and polarized massive operator matrix elements A(Qg)((3)) and Delta A(Qg)((3)) contain first- order factorizable and non-first-order factorizable contributions in the determining difference or differential equations of their master integrals. We compute their first-order factorizable contributions in the single heavy mass case for all contributing Feynman diagrams. Moreover, we present the complete color-zeta factors for the cases in which also non-first-order factorizable contributions emerge in the master integrals, but cancel in the final result as found by using the method of arbitrary high Mellin moments. Individual contributions depend also on generalized harmonic sums and on nested finite binomial and inverse binomial sums in Mellin N-space, and correspondingly, on Kummer-Poincare and square-root valued alphabets in Bjorken-x space. We present a complete discussion of the possibilities of solving the present problem in N-space analytically and we also discuss the limitations in the present case to analytically continue the given N-space expressions to N is an element of C by strict methods. The representation through generating functions allows a well synchronized representation of the first-order factorizable results over a 17-letter alphabet. We finally obtain representations in terms of iterated integrals over the corresponding alphabet in x-space, also containing up to weight w = 5 special constants, which can be rationalized to Kummer-Poincare iterated integrals at special arguments. The analytic x-space representation requires separate analyses for the intervals x is an element of [0,1/4], [1/4,1/2], [1/2,1] and x > 1. We also derive the small and large x limits of the first-order factorizable contributions. Furthermore, we perform comparisons to a number of known Mellin moments, calculated by a different method for the corresponding subset of Feynman diagrams, and an independent high- precision numerical solution of the problems.
| Item Type: | Article |
|---|---|
| Uncontrolled Keywords: | HEAVY FLAVOR CONTRIBUTIONS; STRUCTURE-FUNCTION F-2(X; ORDINARY DIFFERENCE-EQUATIONS; DEEP-INELASTIC SCATTERING; QCD BETA-FUNCTION; SPLITTING FUNCTIONS; HARMONIC SUMS; NUMBER SCHEME; ANOMALOUS DIMENSIONS; WILSON COEFFICIENTS; |
| Subjects: | 500 Science > 530 Physics |
| Divisions: | Physics > Institute of Theroretical Physics |
| Depositing User: | Dr. Gernot Deinzer |
| Date Deposited: | 09 Dec 2025 09:25 |
| Last Modified: | 09 Dec 2025 09:25 |
| URI: | https://pred.uni-regensburg.de/id/eprint/65135 |
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