The LBK theorem to all orders
Abstract We study the soft limit of one-photon radiation at next-to-leading power (NLP) in the framework of heavy-quark effective theory (HQET) to all orders in perturbation theory. We establish the soft theorem that for unpolarised scattering the radiative contribution up to NLP is entirely determi...
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| Format: | Article |
| Language: | English |
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SpringerOpen
2023-07-01
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| Series: | Journal of High Energy Physics |
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| Online Access: | https://doi.org/10.1007/JHEP07(2023)177 |
| _version_ | 1797647495258439680 |
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| author | Tim Engel |
| author_facet | Tim Engel |
| author_sort | Tim Engel |
| collection | DOAJ |
| description | Abstract We study the soft limit of one-photon radiation at next-to-leading power (NLP) in the framework of heavy-quark effective theory (HQET) to all orders in perturbation theory. We establish the soft theorem that for unpolarised scattering the radiative contribution up to NLP is entirely determined by the non-radiative amplitude. This generalises the Low-Burnett-Kroll (LBK) theorem for QED to all orders. All hard matching corrections can be calculated by applying the LBK differential operator to the non-radiative amplitude. The virtual corrections in the effective theory vanish beyond one loop, resulting in a one-loop exact soft function. As a first, non-trivial application we calculate the real-virtual-virtual electron-line corrections to muon-electron scattering at NLP in the soft limit. |
| first_indexed | 2024-03-11T15:18:24Z |
| format | Article |
| id | doaj.art-a2108070f93b49ac9579bb4a7c509647 |
| institution | Directory Open Access Journal |
| issn | 1029-8479 |
| language | English |
| last_indexed | 2024-03-11T15:18:24Z |
| publishDate | 2023-07-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of High Energy Physics |
| spelling | doaj.art-a2108070f93b49ac9579bb4a7c5096472023-10-29T12:06:44ZengSpringerOpenJournal of High Energy Physics1029-84792023-07-012023713210.1007/JHEP07(2023)177The LBK theorem to all ordersTim Engel0Physikalisches Institut, Albert-Ludwigs-Universität FreiburgAbstract We study the soft limit of one-photon radiation at next-to-leading power (NLP) in the framework of heavy-quark effective theory (HQET) to all orders in perturbation theory. We establish the soft theorem that for unpolarised scattering the radiative contribution up to NLP is entirely determined by the non-radiative amplitude. This generalises the Low-Burnett-Kroll (LBK) theorem for QED to all orders. All hard matching corrections can be calculated by applying the LBK differential operator to the non-radiative amplitude. The virtual corrections in the effective theory vanish beyond one loop, resulting in a one-loop exact soft function. As a first, non-trivial application we calculate the real-virtual-virtual electron-line corrections to muon-electron scattering at NLP in the soft limit.https://doi.org/10.1007/JHEP07(2023)177Effective Field TheoriesPrecision QEDScattering Amplitudes |
| spellingShingle | Tim Engel The LBK theorem to all orders Journal of High Energy Physics Effective Field Theories Precision QED Scattering Amplitudes |
| title | The LBK theorem to all orders |
| title_full | The LBK theorem to all orders |
| title_fullStr | The LBK theorem to all orders |
| title_full_unstemmed | The LBK theorem to all orders |
| title_short | The LBK theorem to all orders |
| title_sort | lbk theorem to all orders |
| topic | Effective Field Theories Precision QED Scattering Amplitudes |
| url | https://doi.org/10.1007/JHEP07(2023)177 |
| work_keys_str_mv | AT timengel thelbktheoremtoallorders AT timengel lbktheoremtoallorders |