GKZ hypergeometric systems of the three-loop vacuum Feynman integrals
Abstract We present the Gel’fand-Kapranov-Zelevinsky (GKZ) hypergeometric systems of the Feynman integrals of the three-loop vacuum diagrams with arbitrary masses, basing on Mellin-Barnes representations and Miller’s transformation. The codimension of derived GKZ hypergeometric systems equals the nu...
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| Format: | Article |
| Language: | English |
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SpringerOpen
2023-05-01
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| Series: | Journal of High Energy Physics |
| Subjects: | |
| Online Access: | https://doi.org/10.1007/JHEP05(2023)075 |
| _version_ | 1797736397765869568 |
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| author | Hai-Bin Zhang Tai-Fu Feng |
| author_facet | Hai-Bin Zhang Tai-Fu Feng |
| author_sort | Hai-Bin Zhang |
| collection | DOAJ |
| description | Abstract We present the Gel’fand-Kapranov-Zelevinsky (GKZ) hypergeometric systems of the Feynman integrals of the three-loop vacuum diagrams with arbitrary masses, basing on Mellin-Barnes representations and Miller’s transformation. The codimension of derived GKZ hypergeometric systems equals the number of independent dimensionless ratios among the virtual masses squared. Through GKZ hypergeometric systems, the analytical hypergeometric series solutions can be obtained in neighborhoods of origin including infinity. The linear independent hypergeometric series solutions whose convergent regions have non-empty intersection can constitute a fundamental solution system in a proper subset of the whole parameter space. The analytical expression of the vacuum integral can be formulated as a linear combination of the corresponding fundamental solution system in certain convergent region. |
| first_indexed | 2024-03-12T13:13:12Z |
| format | Article |
| id | doaj.art-327dd757f0cd41b4829585dca7bfed17 |
| institution | Directory Open Access Journal |
| issn | 1029-8479 |
| language | English |
| last_indexed | 2024-03-12T13:13:12Z |
| publishDate | 2023-05-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of High Energy Physics |
| spelling | doaj.art-327dd757f0cd41b4829585dca7bfed172023-08-27T11:06:47ZengSpringerOpenJournal of High Energy Physics1029-84792023-05-012023514210.1007/JHEP05(2023)075GKZ hypergeometric systems of the three-loop vacuum Feynman integralsHai-Bin Zhang0Tai-Fu Feng1Department of Physics, Hebei UniversityDepartment of Physics, Hebei UniversityAbstract We present the Gel’fand-Kapranov-Zelevinsky (GKZ) hypergeometric systems of the Feynman integrals of the three-loop vacuum diagrams with arbitrary masses, basing on Mellin-Barnes representations and Miller’s transformation. The codimension of derived GKZ hypergeometric systems equals the number of independent dimensionless ratios among the virtual masses squared. Through GKZ hypergeometric systems, the analytical hypergeometric series solutions can be obtained in neighborhoods of origin including infinity. The linear independent hypergeometric series solutions whose convergent regions have non-empty intersection can constitute a fundamental solution system in a proper subset of the whole parameter space. The analytical expression of the vacuum integral can be formulated as a linear combination of the corresponding fundamental solution system in certain convergent region.https://doi.org/10.1007/JHEP05(2023)075Higher Order Electroweak CalculationsDifferential and Algebraic GeometryScattering Amplitudes |
| spellingShingle | Hai-Bin Zhang Tai-Fu Feng GKZ hypergeometric systems of the three-loop vacuum Feynman integrals Journal of High Energy Physics Higher Order Electroweak Calculations Differential and Algebraic Geometry Scattering Amplitudes |
| title | GKZ hypergeometric systems of the three-loop vacuum Feynman integrals |
| title_full | GKZ hypergeometric systems of the three-loop vacuum Feynman integrals |
| title_fullStr | GKZ hypergeometric systems of the three-loop vacuum Feynman integrals |
| title_full_unstemmed | GKZ hypergeometric systems of the three-loop vacuum Feynman integrals |
| title_short | GKZ hypergeometric systems of the three-loop vacuum Feynman integrals |
| title_sort | gkz hypergeometric systems of the three loop vacuum feynman integrals |
| topic | Higher Order Electroweak Calculations Differential and Algebraic Geometry Scattering Amplitudes |
| url | https://doi.org/10.1007/JHEP05(2023)075 |
| work_keys_str_mv | AT haibinzhang gkzhypergeometricsystemsofthethreeloopvacuumfeynmanintegrals AT taifufeng gkzhypergeometricsystemsofthethreeloopvacuumfeynmanintegrals |