On positive geometries of quartic interactions: one loop integrands from polytopes
Abstract Building on the seminal work of Arkani-Hamed, He, Salvatori and Thomas (AHST) [1] we explore the positive geometry encoding one loop scattering amplitude for quartic scalar interactions. We define a new class of combinatorial polytopes that we call pseudo-accordiohedra whose poset structure...
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| Format: | Article |
| Language: | English |
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SpringerOpen
2021-07-01
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| Series: | Journal of High Energy Physics |
| Subjects: | |
| Online Access: | https://doi.org/10.1007/JHEP07(2021)136 |
| _version_ | 1818606664268382208 |
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| author | Mrunmay Jagadale Alok Laddha |
| author_facet | Mrunmay Jagadale Alok Laddha |
| author_sort | Mrunmay Jagadale |
| collection | DOAJ |
| description | Abstract Building on the seminal work of Arkani-Hamed, He, Salvatori and Thomas (AHST) [1] we explore the positive geometry encoding one loop scattering amplitude for quartic scalar interactions. We define a new class of combinatorial polytopes that we call pseudo-accordiohedra whose poset structures are associated to singularities of the one loop integrand associated to scalar quartic interactions. Pseudo-accordiohedra parametrize a family of projective forms on the abstract kinematic space defined by AHST and restriction of these forms to the type-D associahedra can be associated to one-loop integrands for quartic interactions. The restriction (of the projective form) can also be thought of as a canonical top form on certain geometric realisations of pseudo-accordiohedra. Our work explores a large class of geometric realisations of the type-D associahedra which include all the AHST realisations. These realisations are based on the pseudo-triangulation model for type-D cluster algebras discovered by Ceballos and Pilaud [2]. |
| first_indexed | 2024-12-16T14:14:27Z |
| format | Article |
| id | doaj.art-ec79cc659fae44c38f3c33dceed281fc |
| institution | Directory Open Access Journal |
| issn | 1029-8479 |
| language | English |
| last_indexed | 2024-12-16T14:14:27Z |
| publishDate | 2021-07-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of High Energy Physics |
| spelling | doaj.art-ec79cc659fae44c38f3c33dceed281fc2022-12-21T22:28:39ZengSpringerOpenJournal of High Energy Physics1029-84792021-07-012021713510.1007/JHEP07(2021)136On positive geometries of quartic interactions: one loop integrands from polytopesMrunmay Jagadale0Alok Laddha1Chennai Mathematical InstituteChennai Mathematical InstituteAbstract Building on the seminal work of Arkani-Hamed, He, Salvatori and Thomas (AHST) [1] we explore the positive geometry encoding one loop scattering amplitude for quartic scalar interactions. We define a new class of combinatorial polytopes that we call pseudo-accordiohedra whose poset structures are associated to singularities of the one loop integrand associated to scalar quartic interactions. Pseudo-accordiohedra parametrize a family of projective forms on the abstract kinematic space defined by AHST and restriction of these forms to the type-D associahedra can be associated to one-loop integrands for quartic interactions. The restriction (of the projective form) can also be thought of as a canonical top form on certain geometric realisations of pseudo-accordiohedra. Our work explores a large class of geometric realisations of the type-D associahedra which include all the AHST realisations. These realisations are based on the pseudo-triangulation model for type-D cluster algebras discovered by Ceballos and Pilaud [2].https://doi.org/10.1007/JHEP07(2021)136Field Theories in Higher DimensionsNonperturbative EffectsScattering Amplitudes |
| spellingShingle | Mrunmay Jagadale Alok Laddha On positive geometries of quartic interactions: one loop integrands from polytopes Journal of High Energy Physics Field Theories in Higher Dimensions Nonperturbative Effects Scattering Amplitudes |
| title | On positive geometries of quartic interactions: one loop integrands from polytopes |
| title_full | On positive geometries of quartic interactions: one loop integrands from polytopes |
| title_fullStr | On positive geometries of quartic interactions: one loop integrands from polytopes |
| title_full_unstemmed | On positive geometries of quartic interactions: one loop integrands from polytopes |
| title_short | On positive geometries of quartic interactions: one loop integrands from polytopes |
| title_sort | on positive geometries of quartic interactions one loop integrands from polytopes |
| topic | Field Theories in Higher Dimensions Nonperturbative Effects Scattering Amplitudes |
| url | https://doi.org/10.1007/JHEP07(2021)136 |
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