A combinatoric shortcut to evaluate CHY-forms
Abstract In our recent work, we proposed a differential operator for the evaluation of the multi-dimensional residues on isolated (zero-dimensional) poles. In this paper we discuss some new insight on evaluating the (generalized) Cachazo-He-Yuan (CHY) forms of the scattering amplitudes using this di...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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SpringerOpen
2017-06-01
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| Series: | Journal of High Energy Physics |
| Subjects: | |
| Online Access: | http://link.springer.com/article/10.1007/JHEP06(2017)015 |
| _version_ | 1818215561172090880 |
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| author | Tianheng Wang Gang Chen Yeuk-Kwan E. Cheung Feng Xu |
| author_facet | Tianheng Wang Gang Chen Yeuk-Kwan E. Cheung Feng Xu |
| author_sort | Tianheng Wang |
| collection | DOAJ |
| description | Abstract In our recent work, we proposed a differential operator for the evaluation of the multi-dimensional residues on isolated (zero-dimensional) poles. In this paper we discuss some new insight on evaluating the (generalized) Cachazo-He-Yuan (CHY) forms of the scattering amplitudes using this differential operator. We introduce a tableau represen-tation for the coefficients appearing in the proposed differential operator. Combining the tableaux with the polynomial form of the scattering equations, the evaluation of the gen-eralized CHY form becomes a simple combinatoric problem. It is thus possible to obtain the coefficients arising in the differential operator in a straightforward way. We present the procedure for a complete solution of the n-gon amplitudes at one-loop level in a generalized CHY form. We also apply our method to fully evaluate the one-loop five-point amplitude in the maximally supersymmetric Yang-Mills theory; the final result is identical to the one obtained by Q-Cut. |
| first_indexed | 2024-12-12T06:38:02Z |
| format | Article |
| id | doaj.art-abe5011bdfe1466aa319405e0083d484 |
| institution | Directory Open Access Journal |
| issn | 1029-8479 |
| language | English |
| last_indexed | 2024-12-12T06:38:02Z |
| publishDate | 2017-06-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of High Energy Physics |
| spelling | doaj.art-abe5011bdfe1466aa319405e0083d4842022-12-22T00:34:26ZengSpringerOpenJournal of High Energy Physics1029-84792017-06-012017612910.1007/JHEP06(2017)015A combinatoric shortcut to evaluate CHY-formsTianheng Wang0Gang Chen1Yeuk-Kwan E. Cheung2Feng Xu3Department of Physics, Nanjing UniversityDepartment of Physics, Zhejiang Normal UniversityDepartment of Physics, Nanjing UniversityWeavi Corporation LimitedAbstract In our recent work, we proposed a differential operator for the evaluation of the multi-dimensional residues on isolated (zero-dimensional) poles. In this paper we discuss some new insight on evaluating the (generalized) Cachazo-He-Yuan (CHY) forms of the scattering amplitudes using this differential operator. We introduce a tableau represen-tation for the coefficients appearing in the proposed differential operator. Combining the tableaux with the polynomial form of the scattering equations, the evaluation of the gen-eralized CHY form becomes a simple combinatoric problem. It is thus possible to obtain the coefficients arising in the differential operator in a straightforward way. We present the procedure for a complete solution of the n-gon amplitudes at one-loop level in a generalized CHY form. We also apply our method to fully evaluate the one-loop five-point amplitude in the maximally supersymmetric Yang-Mills theory; the final result is identical to the one obtained by Q-Cut.http://link.springer.com/article/10.1007/JHEP06(2017)015Scattering AmplitudesDifferential and Algebraic GeometryExtended Supersymmetry |
| spellingShingle | Tianheng Wang Gang Chen Yeuk-Kwan E. Cheung Feng Xu A combinatoric shortcut to evaluate CHY-forms Journal of High Energy Physics Scattering Amplitudes Differential and Algebraic Geometry Extended Supersymmetry |
| title | A combinatoric shortcut to evaluate CHY-forms |
| title_full | A combinatoric shortcut to evaluate CHY-forms |
| title_fullStr | A combinatoric shortcut to evaluate CHY-forms |
| title_full_unstemmed | A combinatoric shortcut to evaluate CHY-forms |
| title_short | A combinatoric shortcut to evaluate CHY-forms |
| title_sort | combinatoric shortcut to evaluate chy forms |
| topic | Scattering Amplitudes Differential and Algebraic Geometry Extended Supersymmetry |
| url | http://link.springer.com/article/10.1007/JHEP06(2017)015 |
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