Pentagon integrals to arbitrary order in the dimensional regulator
Abstract We analytically calculate one-loop five-point Master Integrals, pentagon integrals, with up to one off-shell leg to arbitrary order in the dimensional regulator in d = 4−2𝜖 space-time dimensions. A pure basis of Master Integrals is constructed for the pentagon family with one off-shell leg,...
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| Format: | Article |
| Language: | English |
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SpringerOpen
2021-06-01
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| Series: | Journal of High Energy Physics |
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| Online Access: | https://doi.org/10.1007/JHEP06(2021)037 |
| _version_ | 1818865035269636096 |
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| author | Nikolaos Syrrakos |
| author_facet | Nikolaos Syrrakos |
| author_sort | Nikolaos Syrrakos |
| collection | DOAJ |
| description | Abstract We analytically calculate one-loop five-point Master Integrals, pentagon integrals, with up to one off-shell leg to arbitrary order in the dimensional regulator in d = 4−2𝜖 space-time dimensions. A pure basis of Master Integrals is constructed for the pentagon family with one off-shell leg, satisfying a single-variable canonical differential equation in the Simplified Differential Equations approach. The relevant boundary terms are given in closed form, including a hypergeometric function which can be expanded to arbitrary order in the dimensional regulator using the Mathematica package HypExp. Thus one can obtain solutions of the canonical differential equation in terms of Goncharov Polylogartihms of arbitrary transcendental weight. As a special limit of the one-mass pentagon family, we obtain a fully analytic result for the massless pentagon family in terms of pure and universally transcendental functions. For both families we provide explicit solutions in terms of Goncharov Polylogartihms up to weight four. |
| first_indexed | 2024-12-19T10:41:09Z |
| format | Article |
| id | doaj.art-f54c18b78fed44afa51391c9c117596a |
| institution | Directory Open Access Journal |
| issn | 1029-8479 |
| language | English |
| last_indexed | 2024-12-19T10:41:09Z |
| publishDate | 2021-06-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of High Energy Physics |
| spelling | doaj.art-f54c18b78fed44afa51391c9c117596a2022-12-21T20:25:28ZengSpringerOpenJournal of High Energy Physics1029-84792021-06-012021611310.1007/JHEP06(2021)037Pentagon integrals to arbitrary order in the dimensional regulatorNikolaos Syrrakos0Institute of Nuclear and Particle Physics, NCSR “Demokritos”Abstract We analytically calculate one-loop five-point Master Integrals, pentagon integrals, with up to one off-shell leg to arbitrary order in the dimensional regulator in d = 4−2𝜖 space-time dimensions. A pure basis of Master Integrals is constructed for the pentagon family with one off-shell leg, satisfying a single-variable canonical differential equation in the Simplified Differential Equations approach. The relevant boundary terms are given in closed form, including a hypergeometric function which can be expanded to arbitrary order in the dimensional regulator using the Mathematica package HypExp. Thus one can obtain solutions of the canonical differential equation in terms of Goncharov Polylogartihms of arbitrary transcendental weight. As a special limit of the one-mass pentagon family, we obtain a fully analytic result for the massless pentagon family in terms of pure and universally transcendental functions. For both families we provide explicit solutions in terms of Goncharov Polylogartihms up to weight four.https://doi.org/10.1007/JHEP06(2021)037QCD Phenomenology |
| spellingShingle | Nikolaos Syrrakos Pentagon integrals to arbitrary order in the dimensional regulator Journal of High Energy Physics QCD Phenomenology |
| title | Pentagon integrals to arbitrary order in the dimensional regulator |
| title_full | Pentagon integrals to arbitrary order in the dimensional regulator |
| title_fullStr | Pentagon integrals to arbitrary order in the dimensional regulator |
| title_full_unstemmed | Pentagon integrals to arbitrary order in the dimensional regulator |
| title_short | Pentagon integrals to arbitrary order in the dimensional regulator |
| title_sort | pentagon integrals to arbitrary order in the dimensional regulator |
| topic | QCD Phenomenology |
| url | https://doi.org/10.1007/JHEP06(2021)037 |
| work_keys_str_mv | AT nikolaossyrrakos pentagonintegralstoarbitraryorderinthedimensionalregulator |