Transforming differential equations of multi-loop Feynman integrals into canonical form
Abstract The method of differential equations has been proven to be a powerful tool for the computation of multi-loop Feynman integrals appearing in quantum field theory. It has been observed that in many instances a canonical basis can be chosen, which drastically simplifies the solution of the dif...
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| Format: | Article |
| Language: | English |
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SpringerOpen
2017-04-01
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| Series: | Journal of High Energy Physics |
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| Online Access: | http://link.springer.com/article/10.1007/JHEP04(2017)006 |
| _version_ | 1819077890000551936 |
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| author | Christoph Meyer |
| author_facet | Christoph Meyer |
| author_sort | Christoph Meyer |
| collection | DOAJ |
| description | Abstract The method of differential equations has been proven to be a powerful tool for the computation of multi-loop Feynman integrals appearing in quantum field theory. It has been observed that in many instances a canonical basis can be chosen, which drastically simplifies the solution of the differential equation. In this paper, an algorithm is presented that computes the transformation to a canonical basis, starting from some basis that is, for instance, obtained by the usual integration-by-parts reduction techniques. The algorithm requires the existence of a rational transformation to a canonical basis, but is otherwise completely agnostic about the differential equation. In particular, it is applicable to problems involving multiple scales and allows for a rational dependence on the dimensional regulator. It is demonstrated that the algorithm is suitable for current multi-loop calculations by presenting its successful application to a number of non-trivial examples. |
| first_indexed | 2024-12-21T19:04:23Z |
| format | Article |
| id | doaj.art-e064dd22fa9e49faa94b990cd5b8257d |
| institution | Directory Open Access Journal |
| issn | 1029-8479 |
| language | English |
| last_indexed | 2024-12-21T19:04:23Z |
| publishDate | 2017-04-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of High Energy Physics |
| spelling | doaj.art-e064dd22fa9e49faa94b990cd5b8257d2022-12-21T18:53:24ZengSpringerOpenJournal of High Energy Physics1029-84792017-04-012017414310.1007/JHEP04(2017)006Transforming differential equations of multi-loop Feynman integrals into canonical formChristoph Meyer0Institut für Physik, Humboldt-Universität zu BerlinAbstract The method of differential equations has been proven to be a powerful tool for the computation of multi-loop Feynman integrals appearing in quantum field theory. It has been observed that in many instances a canonical basis can be chosen, which drastically simplifies the solution of the differential equation. In this paper, an algorithm is presented that computes the transformation to a canonical basis, starting from some basis that is, for instance, obtained by the usual integration-by-parts reduction techniques. The algorithm requires the existence of a rational transformation to a canonical basis, but is otherwise completely agnostic about the differential equation. In particular, it is applicable to problems involving multiple scales and allows for a rational dependence on the dimensional regulator. It is demonstrated that the algorithm is suitable for current multi-loop calculations by presenting its successful application to a number of non-trivial examples.http://link.springer.com/article/10.1007/JHEP04(2017)006QCD Phenomenology |
| spellingShingle | Christoph Meyer Transforming differential equations of multi-loop Feynman integrals into canonical form Journal of High Energy Physics QCD Phenomenology |
| title | Transforming differential equations of multi-loop Feynman integrals into canonical form |
| title_full | Transforming differential equations of multi-loop Feynman integrals into canonical form |
| title_fullStr | Transforming differential equations of multi-loop Feynman integrals into canonical form |
| title_full_unstemmed | Transforming differential equations of multi-loop Feynman integrals into canonical form |
| title_short | Transforming differential equations of multi-loop Feynman integrals into canonical form |
| title_sort | transforming differential equations of multi loop feynman integrals into canonical form |
| topic | QCD Phenomenology |
| url | http://link.springer.com/article/10.1007/JHEP04(2017)006 |
| work_keys_str_mv | AT christophmeyer transformingdifferentialequationsofmultiloopfeynmanintegralsintocanonicalform |