Analytical amplitudes from numerical solutions of the scattering equations
Abstract The CHY formalism for massless scattering provides a cohesive framework for the computation of scattering amplitudes in a variety of theories. It is especially compelling because it elucidates existing relations among theories which are seemingly unrelated in a standard Lagrangian formulati...
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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 |
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| Online Access: | http://link.springer.com/article/10.1007/JHEP02(2020)194 |
| _version_ | 1818533956918706176 |
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| author | Giuseppe De Laurentis |
| author_facet | Giuseppe De Laurentis |
| author_sort | Giuseppe De Laurentis |
| collection | DOAJ |
| description | Abstract The CHY formalism for massless scattering provides a cohesive framework for the computation of scattering amplitudes in a variety of theories. It is especially compelling because it elucidates existing relations among theories which are seemingly unrelated in a standard Lagrangian formulation. However, it entails operations that are highly non-trivial to perform analytically, most notably solving the scattering equations. We present a new Python package (seampy1) to solve the scattering equations and to compute scattering amplitudes. Both operations are done numerically with high-precision floating-point algebra. Elimination theory is used to obtain solutions to the scattering equations for arbitrary kinematics. These solutions are then applied to a variety of CHY integrands to obtain tree amplitudes for the following theories: Yang-Mills, Einstein gravity, biadjoint scalar, Born-Infeld, non-linear sigma model, Galileon, conformal gravity and (DF)2. Finally, we exploit this high-precision numerical implementation to explore the singularity structure of the amplitudes and to reconstruct analytical expressions which make manifest their pole structure. Some of the expressions for conformal gravity and the (DF)2 gauge theory are new to the best of our knowledge. |
| first_indexed | 2024-12-11T18:05:33Z |
| format | Article |
| id | doaj.art-327b2adfb62c44869ee5781b418aa04d |
| institution | Directory Open Access Journal |
| issn | 1029-8479 |
| language | English |
| last_indexed | 2024-12-11T18:05:33Z |
| publishDate | 2020-02-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of High Energy Physics |
| spelling | doaj.art-327b2adfb62c44869ee5781b418aa04d2022-12-22T00:55:45ZengSpringerOpenJournal of High Energy Physics1029-84792020-02-012020212810.1007/JHEP02(2020)194Analytical amplitudes from numerical solutions of the scattering equationsGiuseppe De Laurentis0Department of Physics, Durham UniversityAbstract The CHY formalism for massless scattering provides a cohesive framework for the computation of scattering amplitudes in a variety of theories. It is especially compelling because it elucidates existing relations among theories which are seemingly unrelated in a standard Lagrangian formulation. However, it entails operations that are highly non-trivial to perform analytically, most notably solving the scattering equations. We present a new Python package (seampy1) to solve the scattering equations and to compute scattering amplitudes. Both operations are done numerically with high-precision floating-point algebra. Elimination theory is used to obtain solutions to the scattering equations for arbitrary kinematics. These solutions are then applied to a variety of CHY integrands to obtain tree amplitudes for the following theories: Yang-Mills, Einstein gravity, biadjoint scalar, Born-Infeld, non-linear sigma model, Galileon, conformal gravity and (DF)2. Finally, we exploit this high-precision numerical implementation to explore the singularity structure of the amplitudes and to reconstruct analytical expressions which make manifest their pole structure. Some of the expressions for conformal gravity and the (DF)2 gauge theory are new to the best of our knowledge.http://link.springer.com/article/10.1007/JHEP02(2020)194Scattering AmplitudesGauge-gravity correspondence |
| spellingShingle | Giuseppe De Laurentis Analytical amplitudes from numerical solutions of the scattering equations Journal of High Energy Physics Scattering Amplitudes Gauge-gravity correspondence |
| title | Analytical amplitudes from numerical solutions of the scattering equations |
| title_full | Analytical amplitudes from numerical solutions of the scattering equations |
| title_fullStr | Analytical amplitudes from numerical solutions of the scattering equations |
| title_full_unstemmed | Analytical amplitudes from numerical solutions of the scattering equations |
| title_short | Analytical amplitudes from numerical solutions of the scattering equations |
| title_sort | analytical amplitudes from numerical solutions of the scattering equations |
| topic | Scattering Amplitudes Gauge-gravity correspondence |
| url | http://link.springer.com/article/10.1007/JHEP02(2020)194 |
| work_keys_str_mv | AT giuseppedelaurentis analyticalamplitudesfromnumericalsolutionsofthescatteringequations |