Global bases for nonplanar loop integrands, generalized unitarity, and the double copy to all loop orders
Abstract We introduce a constructive method for defining a global loop-integrand basis for scattering amplitudes, encompassing both planar and nonplanar contributions. Our approach utilizes a graph-based framework to establish a well-defined, non-redundant basis of integrands. This basis, constructe...
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| Format: | Article |
| Language: | English |
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SpringerOpen
2025-06-01
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| Series: | Journal of High Energy Physics |
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| Online Access: | https://doi.org/10.1007/JHEP06(2025)115 |
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| author | Zvi Bern Enrico Herrmann Radu Roiban Michael S. Ruf Mao Zeng |
| author_facet | Zvi Bern Enrico Herrmann Radu Roiban Michael S. Ruf Mao Zeng |
| author_sort | Zvi Bern |
| collection | DOAJ |
| description | Abstract We introduce a constructive method for defining a global loop-integrand basis for scattering amplitudes, encompassing both planar and nonplanar contributions. Our approach utilizes a graph-based framework to establish a well-defined, non-redundant basis of integrands. This basis, constructed from a chosen set of non-redundant graphs together with a selection of irreducible scalar products, provides clear insights into various physical properties of scattering amplitudes and proves useful in multiple contexts, such as on-shell Ward identities and manifesting gauge-choice independence. A key advantage of our integrand basis is its ability to streamline the generalized unitarity method. Specifically, we can directly read off the coefficients of basis elements without resorting to ansätze or solving linear equations. This novel approach allows us to lift generalized unitarity cuts — expressed as products of tree amplitudes — to loop-level integrands, facilitating the use of the tree-level double copy to generate complete gravitational integrands at any loop order. This method circumvents the difficulties in identifying complete higher-loop-order gauge-theory integrands that adhere to the color-kinematics duality. Additionally, our cut-based organization is well-suited for expansion in hard or soft limits, aiding in the exploration of ultraviolet or classical limits of scattering amplitudes. |
| format | Article |
| id | doaj-art-e40b8b1c533b4f839b117cf0b680c4ea |
| institution | DOAJ |
| issn | 1029-8479 |
| language | English |
| publishDate | 2025-06-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of High Energy Physics |
| spelling | doaj-art-e40b8b1c533b4f839b117cf0b680c4ea2025-08-20T03:04:21ZengSpringerOpenJournal of High Energy Physics1029-84792025-06-012025615510.1007/JHEP06(2025)115Global bases for nonplanar loop integrands, generalized unitarity, and the double copy to all loop ordersZvi Bern0Enrico Herrmann1Radu Roiban2Michael S. Ruf3Mao Zeng4Mani L. Bhaumik Institute for Theoretical Physics, University of California at Los AngelesMani L. Bhaumik Institute for Theoretical Physics, University of California at Los AngelesInstitute for Gravitation and the Cosmos, Pennsylvania State UniversityMani L. Bhaumik Institute for Theoretical Physics, University of California at Los AngelesSchool of Physics and Astronomy, University of EdinburghAbstract We introduce a constructive method for defining a global loop-integrand basis for scattering amplitudes, encompassing both planar and nonplanar contributions. Our approach utilizes a graph-based framework to establish a well-defined, non-redundant basis of integrands. This basis, constructed from a chosen set of non-redundant graphs together with a selection of irreducible scalar products, provides clear insights into various physical properties of scattering amplitudes and proves useful in multiple contexts, such as on-shell Ward identities and manifesting gauge-choice independence. A key advantage of our integrand basis is its ability to streamline the generalized unitarity method. Specifically, we can directly read off the coefficients of basis elements without resorting to ansätze or solving linear equations. This novel approach allows us to lift generalized unitarity cuts — expressed as products of tree amplitudes — to loop-level integrands, facilitating the use of the tree-level double copy to generate complete gravitational integrands at any loop order. This method circumvents the difficulties in identifying complete higher-loop-order gauge-theory integrands that adhere to the color-kinematics duality. Additionally, our cut-based organization is well-suited for expansion in hard or soft limits, aiding in the exploration of ultraviolet or classical limits of scattering amplitudes.https://doi.org/10.1007/JHEP06(2025)115Scattering AmplitudesEffective Field Theories |
| spellingShingle | Zvi Bern Enrico Herrmann Radu Roiban Michael S. Ruf Mao Zeng Global bases for nonplanar loop integrands, generalized unitarity, and the double copy to all loop orders Journal of High Energy Physics Scattering Amplitudes Effective Field Theories |
| title | Global bases for nonplanar loop integrands, generalized unitarity, and the double copy to all loop orders |
| title_full | Global bases for nonplanar loop integrands, generalized unitarity, and the double copy to all loop orders |
| title_fullStr | Global bases for nonplanar loop integrands, generalized unitarity, and the double copy to all loop orders |
| title_full_unstemmed | Global bases for nonplanar loop integrands, generalized unitarity, and the double copy to all loop orders |
| title_short | Global bases for nonplanar loop integrands, generalized unitarity, and the double copy to all loop orders |
| title_sort | global bases for nonplanar loop integrands generalized unitarity and the double copy to all loop orders |
| topic | Scattering Amplitudes Effective Field Theories |
| url | https://doi.org/10.1007/JHEP06(2025)115 |
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