Bootstrapping pentagon functions
Abstract In Phys. Rev. Lett. 116 (2016) 062001, the space of planar pentagon functions that describes all two-loop on-shell five-particle scattering amplitudes was introduced. In the present paper we present a natural extension of this space to non-planar pentagon functions. This provides the basis...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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SpringerOpen
2018-05-01
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| Series: | Journal of High Energy Physics |
| Subjects: | |
| Online Access: | http://link.springer.com/article/10.1007/JHEP05(2018)164 |
| _version_ | 1819225064423292928 |
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| author | Dmitry Chicherin Johannes Henn Vladimir Mitev |
| author_facet | Dmitry Chicherin Johannes Henn Vladimir Mitev |
| author_sort | Dmitry Chicherin |
| collection | DOAJ |
| description | Abstract In Phys. Rev. Lett. 116 (2016) 062001, the space of planar pentagon functions that describes all two-loop on-shell five-particle scattering amplitudes was introduced. In the present paper we present a natural extension of this space to non-planar pentagon functions. This provides the basis for our pentagon bootstrap program. We classify the relevant functions up to weight four, which is relevant for two-loop scattering amplitudes. We constrain the first entry of the symbol of the functions using information on branch cuts. Drawing on an analogy from the planar case, we introduce a conjectural second-entry condition on the symbol. We then show that the information on the function space, when complemented with some additional insights, can be used to efficiently bootstrap individual Feynman integrals. The extra information is read off of Mellin-Barnes representations of the integrals, either by evaluating simple asymptotic limits, or by taking discontinuities in the kinematic variables. We use this method to evaluate the symbols of two non-trivial non-planar five-particle integrals, up to and including the finite part. |
| first_indexed | 2024-12-23T10:03:39Z |
| format | Article |
| id | doaj.art-0866c2ab1f574732b9af5d30ae444cd6 |
| institution | Directory Open Access Journal |
| issn | 1029-8479 |
| language | English |
| last_indexed | 2024-12-23T10:03:39Z |
| publishDate | 2018-05-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of High Energy Physics |
| spelling | doaj.art-0866c2ab1f574732b9af5d30ae444cd62022-12-21T17:51:09ZengSpringerOpenJournal of High Energy Physics1029-84792018-05-012018512710.1007/JHEP05(2018)164Bootstrapping pentagon functionsDmitry Chicherin0Johannes Henn1Vladimir Mitev2PRISMA Cluster of Excellence, Johannes Gutenberg UniversityPRISMA Cluster of Excellence, Johannes Gutenberg UniversityPRISMA Cluster of Excellence, Johannes Gutenberg UniversityAbstract In Phys. Rev. Lett. 116 (2016) 062001, the space of planar pentagon functions that describes all two-loop on-shell five-particle scattering amplitudes was introduced. In the present paper we present a natural extension of this space to non-planar pentagon functions. This provides the basis for our pentagon bootstrap program. We classify the relevant functions up to weight four, which is relevant for two-loop scattering amplitudes. We constrain the first entry of the symbol of the functions using information on branch cuts. Drawing on an analogy from the planar case, we introduce a conjectural second-entry condition on the symbol. We then show that the information on the function space, when complemented with some additional insights, can be used to efficiently bootstrap individual Feynman integrals. The extra information is read off of Mellin-Barnes representations of the integrals, either by evaluating simple asymptotic limits, or by taking discontinuities in the kinematic variables. We use this method to evaluate the symbols of two non-trivial non-planar five-particle integrals, up to and including the finite part.http://link.springer.com/article/10.1007/JHEP05(2018)164Scattering AmplitudesPerturbative QCD |
| spellingShingle | Dmitry Chicherin Johannes Henn Vladimir Mitev Bootstrapping pentagon functions Journal of High Energy Physics Scattering Amplitudes Perturbative QCD |
| title | Bootstrapping pentagon functions |
| title_full | Bootstrapping pentagon functions |
| title_fullStr | Bootstrapping pentagon functions |
| title_full_unstemmed | Bootstrapping pentagon functions |
| title_short | Bootstrapping pentagon functions |
| title_sort | bootstrapping pentagon functions |
| topic | Scattering Amplitudes Perturbative QCD |
| url | http://link.springer.com/article/10.1007/JHEP05(2018)164 |
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