Two-loop scattering amplitudes from the Riemann sphere
The scattering equations give striking formulas for massless scattering amplitudes at tree level and, as shown recently, at one loop. The progress at loop level was based on ambitwistor-string theory, which naturally yields the scattering equations. We proposed that, for ambitwistor strings, the sta...
| প্রধান লেখক: | , , , |
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| বিন্যাস: | Journal article |
| প্রকাশিত: |
American Physical Society
2016
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| _version_ | 1826264408713592832 |
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| author | Geyer, Y Mason, L Monteiro, R Tourkine, P |
| author_facet | Geyer, Y Mason, L Monteiro, R Tourkine, P |
| author_sort | Geyer, Y |
| collection | OXFORD |
| description | The scattering equations give striking formulas for massless scattering amplitudes at tree level and, as shown recently, at one loop. The progress at loop level was based on ambitwistor-string theory, which naturally yields the scattering equations. We proposed that, for ambitwistor strings, the standard loop expansion in terms of the genus of the world sheet is equivalent to an expansion in terms of nodes of a Riemann sphere, with the nodes carrying the loop momenta. In this paper, we show how to obtain two-loop scattering equations with the correct factorization properties. We adapt genus-two integrands from the ambitwistor string to the nodal Riemann sphere and show that these yield correct answers, by matching standard results for the four-point two-loop amplitudes of maximal supergravity and super-Yang-Mills theory. In the Yang-Mills case, this requires the loop analogue of the Parke-Taylor factor carrying the color dependence, which includes nonplanar contributions. |
| first_indexed | 2024-03-06T20:07:19Z |
| format | Journal article |
| id | oxford-uuid:29554cd8-6fa5-44a8-a3c9-e2a3b18dad01 |
| institution | University of Oxford |
| last_indexed | 2024-03-06T20:07:19Z |
| publishDate | 2016 |
| publisher | American Physical Society |
| record_format | dspace |
| spelling | oxford-uuid:29554cd8-6fa5-44a8-a3c9-e2a3b18dad012022-03-26T12:18:32ZTwo-loop scattering amplitudes from the Riemann sphereJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:29554cd8-6fa5-44a8-a3c9-e2a3b18dad01Symplectic Elements at OxfordAmerican Physical Society2016Geyer, YMason, LMonteiro, RTourkine, PThe scattering equations give striking formulas for massless scattering amplitudes at tree level and, as shown recently, at one loop. The progress at loop level was based on ambitwistor-string theory, which naturally yields the scattering equations. We proposed that, for ambitwistor strings, the standard loop expansion in terms of the genus of the world sheet is equivalent to an expansion in terms of nodes of a Riemann sphere, with the nodes carrying the loop momenta. In this paper, we show how to obtain two-loop scattering equations with the correct factorization properties. We adapt genus-two integrands from the ambitwistor string to the nodal Riemann sphere and show that these yield correct answers, by matching standard results for the four-point two-loop amplitudes of maximal supergravity and super-Yang-Mills theory. In the Yang-Mills case, this requires the loop analogue of the Parke-Taylor factor carrying the color dependence, which includes nonplanar contributions. |
| spellingShingle | Geyer, Y Mason, L Monteiro, R Tourkine, P Two-loop scattering amplitudes from the Riemann sphere |
| title | Two-loop scattering amplitudes from the Riemann sphere |
| title_full | Two-loop scattering amplitudes from the Riemann sphere |
| title_fullStr | Two-loop scattering amplitudes from the Riemann sphere |
| title_full_unstemmed | Two-loop scattering amplitudes from the Riemann sphere |
| title_short | Two-loop scattering amplitudes from the Riemann sphere |
| title_sort | two loop scattering amplitudes from the riemann sphere |
| work_keys_str_mv | AT geyery twoloopscatteringamplitudesfromtheriemannsphere AT masonl twoloopscatteringamplitudesfromtheriemannsphere AT monteiror twoloopscatteringamplitudesfromtheriemannsphere AT tourkinep twoloopscatteringamplitudesfromtheriemannsphere |