Three-loop contributions to the ρ parameter and iterated integrals of modular forms
Abstract We compute fully analytic results for the three-loop diagrams involving two different massive quark flavours contributing to the ρ parameter in the Standard Model. We find that the results involve exactly the same class of functions that appears in the well-known sunrise and banana graphs,...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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SpringerOpen
2020-02-01
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| Series: | Journal of High Energy Physics |
| Subjects: | |
| Online Access: | https://doi.org/10.1007/JHEP02(2020)050 |
| _version_ | 1818451578809483264 |
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| author | Samuel Abreu Matteo Becchetti Claude Duhr Robin Marzucca |
| author_facet | Samuel Abreu Matteo Becchetti Claude Duhr Robin Marzucca |
| author_sort | Samuel Abreu |
| collection | DOAJ |
| description | Abstract We compute fully analytic results for the three-loop diagrams involving two different massive quark flavours contributing to the ρ parameter in the Standard Model. We find that the results involve exactly the same class of functions that appears in the well-known sunrise and banana graphs, namely elliptic polylogarithms and iterated integrals of modular forms. Using recent developments in the understanding of these functions, we analytically continue all the iterated integrals of modular forms to all regions of the parameter space, and in each region we obtain manifestly real and fast-converging series expansions for these functions. |
| first_indexed | 2024-12-14T21:09:26Z |
| format | Article |
| id | doaj.art-5cdb8ec74e5e4c70b11ce39afbfbc1c6 |
| institution | Directory Open Access Journal |
| issn | 1029-8479 |
| language | English |
| last_indexed | 2024-12-14T21:09:26Z |
| publishDate | 2020-02-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of High Energy Physics |
| spelling | doaj.art-5cdb8ec74e5e4c70b11ce39afbfbc1c62022-12-21T22:47:18ZengSpringerOpenJournal of High Energy Physics1029-84792020-02-012020213810.1007/JHEP02(2020)050Three-loop contributions to the ρ parameter and iterated integrals of modular formsSamuel Abreu0Matteo Becchetti1Claude Duhr2Robin Marzucca3Center for Cosmology, Particle Physics and Phenomenology (CP3), Université Catholique de LouvainCenter for Cosmology, Particle Physics and Phenomenology (CP3), Université Catholique de LouvainTheoretical Physics Department, CERNIPPP, Department of Physics, Durham UniversityAbstract We compute fully analytic results for the three-loop diagrams involving two different massive quark flavours contributing to the ρ parameter in the Standard Model. We find that the results involve exactly the same class of functions that appears in the well-known sunrise and banana graphs, namely elliptic polylogarithms and iterated integrals of modular forms. Using recent developments in the understanding of these functions, we analytically continue all the iterated integrals of modular forms to all regions of the parameter space, and in each region we obtain manifestly real and fast-converging series expansions for these functions.https://doi.org/10.1007/JHEP02(2020)050Perturbative QCDScattering Amplitudes |
| spellingShingle | Samuel Abreu Matteo Becchetti Claude Duhr Robin Marzucca Three-loop contributions to the ρ parameter and iterated integrals of modular forms Journal of High Energy Physics Perturbative QCD Scattering Amplitudes |
| title | Three-loop contributions to the ρ parameter and iterated integrals of modular forms |
| title_full | Three-loop contributions to the ρ parameter and iterated integrals of modular forms |
| title_fullStr | Three-loop contributions to the ρ parameter and iterated integrals of modular forms |
| title_full_unstemmed | Three-loop contributions to the ρ parameter and iterated integrals of modular forms |
| title_short | Three-loop contributions to the ρ parameter and iterated integrals of modular forms |
| title_sort | three loop contributions to the ρ parameter and iterated integrals of modular forms |
| topic | Perturbative QCD Scattering Amplitudes |
| url | https://doi.org/10.1007/JHEP02(2020)050 |
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