The first–order factorizable contributions to the three–loop massive operator matrix elements AQg(3) and ΔAQg(3)
The unpolarized and polarized massive operator matrix elements AQg(3) and ΔAQg(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...
| Main Authors: | , , , , , , |
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| Format: | Article |
| Language: | English |
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Elsevier
2024-02-01
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| Series: | Nuclear Physics B |
| Online Access: | http://www.sciencedirect.com/science/article/pii/S0550321323003541 |
| _version_ | 1827357889758494720 |
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| author | J. Ablinger A. Behring J. Blümlein A. De Freitas A. von Manteuffel C. Schneider K. Schönwald |
| author_facet | J. Ablinger A. Behring J. Blümlein A. De Freitas A. von Manteuffel C. Schneider K. Schönwald |
| author_sort | J. Ablinger |
| collection | DOAJ |
| description | The unpolarized and polarized massive operator matrix elements AQg(3) and ΔAQg(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–ζ 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–Poincaré 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∈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–Poincaré iterated integrals at special arguments. The analytic x–space representation requires separate analyses for the intervals x∈[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. |
| first_indexed | 2024-03-08T05:55:38Z |
| format | Article |
| id | doaj.art-6a76932d56984076b0cdabc24e54530c |
| institution | Directory Open Access Journal |
| issn | 0550-3213 |
| language | English |
| last_indexed | 2024-03-08T05:55:38Z |
| publishDate | 2024-02-01 |
| publisher | Elsevier |
| record_format | Article |
| series | Nuclear Physics B |
| spelling | doaj.art-6a76932d56984076b0cdabc24e54530c2024-02-05T04:30:51ZengElsevierNuclear Physics B0550-32132024-02-01999116427The first–order factorizable contributions to the three–loop massive operator matrix elements AQg(3) and ΔAQg(3)J. Ablinger0A. Behring1J. Blümlein2A. De Freitas3A. von Manteuffel4C. Schneider5K. Schönwald6Johannes Kepler University, Research Institute for Symbolic Computation (RISC), Altenberger Straße 69, A-4040, Linz, Austria; Johann Radon Institute for Computational and Applied Mathematics (RICAM), Austrian Academy of Sciences, Altenberger Straße 69, A-4040 Linz AustriaTheoretical Physics Department, CERN, 1211 Geneva 23, Switzerland; Deutsches Elektronen-Synchrotron DESY, Platanenallee 6, 15738 Zeuthen, GermanyDeutsches Elektronen-Synchrotron DESY, Platanenallee 6, 15738 Zeuthen, Germany; Corresponding author.Deutsches Elektronen-Synchrotron DESY, Platanenallee 6, 15738 Zeuthen, Germany; Johannes Kepler University, Research Institute for Symbolic Computation (RISC), Altenberger Straße 69, A-4040, Linz, AustriaInstitut für Theoretische Physik, Universität Regensburg, 93040 Regensburg, Germany; Department of Physics and Astronomy, Michigan State University, East Lansing, MI 48824, USAJohannes Kepler University, Research Institute for Symbolic Computation (RISC), Altenberger Straße 69, A-4040, Linz, AustriaPhysik-Institut, Universität Zürich, Winterthurerstrasse 190, CH-8057 Zürich, SwitzerlandThe unpolarized and polarized massive operator matrix elements AQg(3) and ΔAQg(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–ζ 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–Poincaré 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∈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–Poincaré iterated integrals at special arguments. The analytic x–space representation requires separate analyses for the intervals x∈[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.http://www.sciencedirect.com/science/article/pii/S0550321323003541 |
| spellingShingle | J. Ablinger A. Behring J. Blümlein A. De Freitas A. von Manteuffel C. Schneider K. Schönwald The first–order factorizable contributions to the three–loop massive operator matrix elements AQg(3) and ΔAQg(3) Nuclear Physics B |
| title | The first–order factorizable contributions to the three–loop massive operator matrix elements AQg(3) and ΔAQg(3) |
| title_full | The first–order factorizable contributions to the three–loop massive operator matrix elements AQg(3) and ΔAQg(3) |
| title_fullStr | The first–order factorizable contributions to the three–loop massive operator matrix elements AQg(3) and ΔAQg(3) |
| title_full_unstemmed | The first–order factorizable contributions to the three–loop massive operator matrix elements AQg(3) and ΔAQg(3) |
| title_short | The first–order factorizable contributions to the three–loop massive operator matrix elements AQg(3) and ΔAQg(3) |
| title_sort | first order factorizable contributions to the three loop massive operator matrix elements aqg 3 and δaqg 3 |
| url | http://www.sciencedirect.com/science/article/pii/S0550321323003541 |
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