The electroweak effective field theory from on-shell amplitudes
Abstract We apply on-shell methods to the bottom-up construction of electroweak amplitudes, allowing for both renormalizable and non-renormalizable interactions. We use the little-group covariant massive-spinor formalism, and flesh out some of its details along the way. Thanks to the compact form of...
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| Format: | Article |
| Language: | English |
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SpringerOpen
2020-01-01
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| Series: | Journal of High Energy Physics |
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| Online Access: | https://doi.org/10.1007/JHEP01(2020)119 |
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| author | Gauthier Durieux Teppei Kitahara Yael Shadmi Yaniv Weiss |
| author_facet | Gauthier Durieux Teppei Kitahara Yael Shadmi Yaniv Weiss |
| author_sort | Gauthier Durieux |
| collection | DOAJ |
| description | Abstract We apply on-shell methods to the bottom-up construction of electroweak amplitudes, allowing for both renormalizable and non-renormalizable interactions. We use the little-group covariant massive-spinor formalism, and flesh out some of its details along the way. Thanks to the compact form of the resulting amplitudes, many of their properties, and in particular the constraints of perturbative unitarity, are easily seen in this formalism. Our approach is purely bottom-up, assuming just the standard-model electroweak spectrum as well as the conservation of electric charge and fermion number. The most general massive three-point amplitudes consistent with these symmetries are derived and studied in detail, as the primary building blocks for the construction of scattering amplitudes. We employ a simple argument, based on tree-level unitarity of four-point amplitudes, to identify the three-point amplitudes that are non-renormalizable at tree level. This bottom-up analysis remarkably reproduces many low-energy relations implied by electroweak symmetry through the standard-model Higgs mechanism and beyond it. We then discuss four-point amplitudes. The gluing of three-point amplitudes into four-point amplitudes in the massive spinor helicity formalism is clarified. As an example, we work out the ψcψ Zh amplitude, including also the non-factorizable part. The latter is an all-order expression in the effective-field-theory expansion. Further constraints on the couplings are obtained by requiring perturbative unitarity. In the ψcψ Zh example, one for instance obtains the renormalizable-level relations between vector and fermion masses and gauge and Yukawa couplings. We supplement our bottom-up derivations with a matching of three- and fourpoint amplitude coefficients onto the standard-model effective field theory (SMEFT) in the broken electroweak phase. This establishes the correspondence with the usual Lagrangian approach and paves the way for SMEFT computations in the on-shell formalism. |
| format | Article |
| id | doaj-art-10aedf7209a94e9d98abb6ee5f4e0d60 |
| institution | Kabale University |
| issn | 1029-8479 |
| language | English |
| publishDate | 2020-01-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of High Energy Physics |
| spelling | doaj-art-10aedf7209a94e9d98abb6ee5f4e0d602025-01-26T12:11:08ZengSpringerOpenJournal of High Energy Physics1029-84792020-01-012020115810.1007/JHEP01(2020)119The electroweak effective field theory from on-shell amplitudesGauthier Durieux0Teppei Kitahara1Yael Shadmi2Yaniv Weiss3Physics Department, Technion — Israel Institute of Technology, Technion CityPhysics Department, Technion — Israel Institute of Technology, Technion CityPhysics Department, Technion — Israel Institute of Technology, Technion CityPhysics Department, Technion — Israel Institute of Technology, Technion CityAbstract We apply on-shell methods to the bottom-up construction of electroweak amplitudes, allowing for both renormalizable and non-renormalizable interactions. We use the little-group covariant massive-spinor formalism, and flesh out some of its details along the way. Thanks to the compact form of the resulting amplitudes, many of their properties, and in particular the constraints of perturbative unitarity, are easily seen in this formalism. Our approach is purely bottom-up, assuming just the standard-model electroweak spectrum as well as the conservation of electric charge and fermion number. The most general massive three-point amplitudes consistent with these symmetries are derived and studied in detail, as the primary building blocks for the construction of scattering amplitudes. We employ a simple argument, based on tree-level unitarity of four-point amplitudes, to identify the three-point amplitudes that are non-renormalizable at tree level. This bottom-up analysis remarkably reproduces many low-energy relations implied by electroweak symmetry through the standard-model Higgs mechanism and beyond it. We then discuss four-point amplitudes. The gluing of three-point amplitudes into four-point amplitudes in the massive spinor helicity formalism is clarified. As an example, we work out the ψcψ Zh amplitude, including also the non-factorizable part. The latter is an all-order expression in the effective-field-theory expansion. Further constraints on the couplings are obtained by requiring perturbative unitarity. In the ψcψ Zh example, one for instance obtains the renormalizable-level relations between vector and fermion masses and gauge and Yukawa couplings. We supplement our bottom-up derivations with a matching of three- and fourpoint amplitude coefficients onto the standard-model effective field theory (SMEFT) in the broken electroweak phase. This establishes the correspondence with the usual Lagrangian approach and paves the way for SMEFT computations in the on-shell formalism.https://doi.org/10.1007/JHEP01(2020)119Effective Field TheoriesScattering AmplitudesSpontaneous Symmetry Breaking |
| spellingShingle | Gauthier Durieux Teppei Kitahara Yael Shadmi Yaniv Weiss The electroweak effective field theory from on-shell amplitudes Journal of High Energy Physics Effective Field Theories Scattering Amplitudes Spontaneous Symmetry Breaking |
| title | The electroweak effective field theory from on-shell amplitudes |
| title_full | The electroweak effective field theory from on-shell amplitudes |
| title_fullStr | The electroweak effective field theory from on-shell amplitudes |
| title_full_unstemmed | The electroweak effective field theory from on-shell amplitudes |
| title_short | The electroweak effective field theory from on-shell amplitudes |
| title_sort | electroweak effective field theory from on shell amplitudes |
| topic | Effective Field Theories Scattering Amplitudes Spontaneous Symmetry Breaking |
| url | https://doi.org/10.1007/JHEP01(2020)119 |
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