Graded transcendental functions: an application to four-point amplitudes with one off-shell leg
Abstract Several recent works have demonstrated the powerful algebraic simplifications that can be achieved for scattering amplitudes through a systematic grading of transcendental quantities. We develop these concepts to construct a minimal basis of functions tailored to a scattering amplitude in a...
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| Format: | Article |
| Language: | English |
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SpringerOpen
2024-12-01
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| Series: | Journal of High Energy Physics |
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| Online Access: | https://doi.org/10.1007/JHEP12(2024)215 |
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| author | Thomas Gehrmann Johannes Henn Petr Jakubčík Jungwon Lim Cesare Carlo Mella Nikolaos Syrrakos Lorenzo Tancredi William J. Torres Bobadilla |
| author_facet | Thomas Gehrmann Johannes Henn Petr Jakubčík Jungwon Lim Cesare Carlo Mella Nikolaos Syrrakos Lorenzo Tancredi William J. Torres Bobadilla |
| author_sort | Thomas Gehrmann |
| collection | DOAJ |
| description | Abstract Several recent works have demonstrated the powerful algebraic simplifications that can be achieved for scattering amplitudes through a systematic grading of transcendental quantities. We develop these concepts to construct a minimal basis of functions tailored to a scattering amplitude in a general way. Starting with formal solutions for all master integral topologies, we organise the appearing functions by properties such as their symbol alphabet or letter adjacency. We rotate the basis such that functions with spurious features appear in the least possible number of basis elements. Since their coefficients must vanish for physical quantities, this approach avoids complex cancellations. As a first application, we evaluate all integral topologies relevant to the three-loop Hggg and Hgq q ¯ $$ Hgq\overline{q} $$ amplitudes in the leading-colour approximation and heavy-top limit. We describe the derivation of canonical differential equation systems and present a method for fixing boundary conditions without the need for a full functional representation. Using multiple numerical reductions, we test the maximal transcendentality conjecture for Hggg and identify a new letter which appears in functions of weight 4 and 5. In addition, we provide the first direct analytic computation of a three-point form factor of the operator Tr(ϕ 2) in planar N $$ \mathcal{N} $$ = 4 sYM and find agreement with numerical and bootstrapped results. |
| format | Article |
| id | doaj-art-663b846b9aeb4cf2999dbc3d77a8e66a |
| institution | Kabale University |
| issn | 1029-8479 |
| language | English |
| publishDate | 2024-12-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of High Energy Physics |
| spelling | doaj-art-663b846b9aeb4cf2999dbc3d77a8e66a2025-01-05T12:05:41ZengSpringerOpenJournal of High Energy Physics1029-84792024-12-0120241214610.1007/JHEP12(2024)215Graded transcendental functions: an application to four-point amplitudes with one off-shell legThomas Gehrmann0Johannes Henn1Petr Jakubčík2Jungwon Lim3Cesare Carlo Mella4Nikolaos Syrrakos5Lorenzo Tancredi6William J. Torres Bobadilla7Physik-Institut, Universität ZurichMax-Planck-Institut für Physik, Werner-Heisenberg-InstitutPhysik-Institut, Universität ZurichMax-Planck-Institut für Physik, Werner-Heisenberg-InstitutTechnical University of Munich, TUM School of Natural Sciences, Physics DepartmentTechnical University of Munich, TUM School of Natural Sciences, Physics DepartmentTechnical University of Munich, TUM School of Natural Sciences, Physics DepartmentDepartment of Mathematical Sciences, University of LiverpoolAbstract Several recent works have demonstrated the powerful algebraic simplifications that can be achieved for scattering amplitudes through a systematic grading of transcendental quantities. We develop these concepts to construct a minimal basis of functions tailored to a scattering amplitude in a general way. Starting with formal solutions for all master integral topologies, we organise the appearing functions by properties such as their symbol alphabet or letter adjacency. We rotate the basis such that functions with spurious features appear in the least possible number of basis elements. Since their coefficients must vanish for physical quantities, this approach avoids complex cancellations. As a first application, we evaluate all integral topologies relevant to the three-loop Hggg and Hgq q ¯ $$ Hgq\overline{q} $$ amplitudes in the leading-colour approximation and heavy-top limit. We describe the derivation of canonical differential equation systems and present a method for fixing boundary conditions without the need for a full functional representation. Using multiple numerical reductions, we test the maximal transcendentality conjecture for Hggg and identify a new letter which appears in functions of weight 4 and 5. In addition, we provide the first direct analytic computation of a three-point form factor of the operator Tr(ϕ 2) in planar N $$ \mathcal{N} $$ = 4 sYM and find agreement with numerical and bootstrapped results.https://doi.org/10.1007/JHEP12(2024)215Higgs ProductionScattering AmplitudesSpecific QCD Phenomenology |
| spellingShingle | Thomas Gehrmann Johannes Henn Petr Jakubčík Jungwon Lim Cesare Carlo Mella Nikolaos Syrrakos Lorenzo Tancredi William J. Torres Bobadilla Graded transcendental functions: an application to four-point amplitudes with one off-shell leg Journal of High Energy Physics Higgs Production Scattering Amplitudes Specific QCD Phenomenology |
| title | Graded transcendental functions: an application to four-point amplitudes with one off-shell leg |
| title_full | Graded transcendental functions: an application to four-point amplitudes with one off-shell leg |
| title_fullStr | Graded transcendental functions: an application to four-point amplitudes with one off-shell leg |
| title_full_unstemmed | Graded transcendental functions: an application to four-point amplitudes with one off-shell leg |
| title_short | Graded transcendental functions: an application to four-point amplitudes with one off-shell leg |
| title_sort | graded transcendental functions an application to four point amplitudes with one off shell leg |
| topic | Higgs Production Scattering Amplitudes Specific QCD Phenomenology |
| url | https://doi.org/10.1007/JHEP12(2024)215 |
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