We derive the contact terms contributing to the four-point amplitudes of the standard model particles, keeping terms with up to quartic energy growth. Imposing just the unbroken low-energy symmetry, and treating the electroweak gauge bosons and the Higgs as independent degrees of freedom, we obtain the most general four-point contact-term amplitudes, corresponding to the Higgs Effective Field Theory (HEFT) framework. The contact terms are spanned by a basis of Stripped Contact Terms, which carry the polarization information, multiplied by polynomials in the Mandelstam invariants. For terms with quadratic energy growth, we also derive the low-energy Standard Model Effective Field Theory (SMEFT) predictions, via on-shell Higgsing of the massless SMEFT contact terms. We discuss several aspects of bottom-up versus top-down on-shell derivations of the HEFT and SMEFT amplitudes, highlighting in particular the simple counting of HEFT dimensions in the on-shell approach and the transparent relation between perturbative unitarity and gauge-invariance in the little-group covariant massive spinor formalism. Our results provide a formulation of Effective Field Theory analyses directly in terms of observable quantities. For terms with quadratic energy growth, we also provide the mapping to the Warsaw basis.
{ "_oai": { "updated": "2023-08-24T00:31:35Z", "id": "oai:repo.scoap3.org:78003", "sets": [ "JHEP" ] }, "authors": [ { "affiliations": [ { "country": "Israel", "value": "Physics Department, Technion \u2014 Israel Institute of Technology, Technion city, Haifa, 3200003, Israel", "organization": "Physics Department, Technion \u2014 Israel Institute of Technology" } ], "surname": "Liu", "email": "liu.hongkai@campus.technion.ac.il", "full_name": "Liu, Hongkai", "given_names": "Hongkai" }, { "affiliations": [ { "country": "Israel", "value": "Physics Department, Technion \u2014 Israel Institute of Technology, Technion city, Haifa, 3200003, Israel", "organization": "Physics Department, Technion \u2014 Israel Institute of Technology" }, { "country": "Spain", "value": "Department of Physics and IFAE-BIST, Universitat Aut\u00f2noma de Barcelona, E-08193 Bellaterra, Barcelona, Spain", "organization": "Universitat Aut\u00f2noma de Barcelona" } ], "surname": "Ma", "email": "tma@ifae.es", "full_name": "Ma, Teng", "given_names": "Teng" }, { "affiliations": [ { "country": "Israel", "value": "Physics Department, Technion \u2014 Israel Institute of Technology, Technion city, Haifa, 3200003, Israel", "organization": "Physics Department, Technion \u2014 Israel Institute of Technology" } ], "surname": "Shadmi", "email": "yshadmi@physics.technion.ac.il", "full_name": "Shadmi, Yael", "given_names": "Yael" }, { "affiliations": [ { "country": "Israel", "value": "Physics Department, Technion \u2014 Israel Institute of Technology, Technion city, Haifa, 3200003, Israel", "organization": "Physics Department, Technion \u2014 Israel Institute of Technology" } ], "surname": "Waterbury", "email": "mwaterbury@campus.technion.ac.il", "full_name": "Waterbury, Michael", "given_names": "Michael" } ], "titles": [ { "source": "Springer", "title": "An EFT hunter\u2019s guide to two-to-two scattering: HEFT and SMEFT on-shell amplitudes" } ], "dois": [ { "value": "10.1007/JHEP05(2023)241" } ], "publication_info": [ { "page_end": "33", "journal_title": "Journal of High Energy Physics", "material": "article", "journal_volume": "2023", "artid": "JHEP05(2023)241", "year": 2023, "page_start": "1", "journal_issue": "5" } ], "$schema": "http://repo.scoap3.org/schemas/hep.json", "acquisition_source": { "date": "2023-08-24T00:30:59.865007", "source": "Springer", "method": "Springer", "submission_number": "5c13f3c8421511ee91ac6ee2827c7def" }, "page_nr": [ 33 ], "license": [ { "url": "https://creativecommons.org/licenses//by/4.0", "license": "CC-BY-4.0" } ], "copyright": [ { "holder": "The Author(s)", "year": "2023" } ], "control_number": "78003", "record_creation_date": "2023-05-31T18:30:11.395138", "_files": [ { "checksum": "md5:2aecc6fcee99b4633ca6df19e14b4f99", "filetype": "xml", "bucket": "06dffaf4-3c54-477f-8b2e-224e144fd106", "version_id": "b428127b-a194-488b-9a3e-b75dcb95b6b4", "key": "10.1007/JHEP05(2023)241.xml", "size": 12116 }, { "checksum": "md5:a2264c3524d975c9338758d5d5afeffa", "filetype": "pdf/a", "bucket": "06dffaf4-3c54-477f-8b2e-224e144fd106", "version_id": "c74e2f1e-8a11-4a4a-8660-df52092e601c", "key": "10.1007/JHEP05(2023)241_a.pdf", "size": 540608 } ], "collections": [ { "primary": "Journal of High Energy Physics" } ], "arxiv_eprints": [ { "categories": [ "hep-ph", "hep-th" ], "value": "2301.11349" } ], "abstracts": [ { "source": "Springer", "value": "We derive the contact terms contributing to the four-point amplitudes of the standard model particles, keeping terms with up to quartic energy growth. Imposing just the unbroken low-energy symmetry, and treating the electroweak gauge bosons and the Higgs as independent degrees of freedom, we obtain the most general four-point contact-term amplitudes, corresponding to the Higgs Effective Field Theory (HEFT) framework. The contact terms are spanned by a basis of Stripped Contact Terms, which carry the polarization information, multiplied by polynomials in the Mandelstam invariants. For terms with quadratic energy growth, we also derive the low-energy Standard Model Effective Field Theory (SMEFT) predictions, via on-shell Higgsing of the massless SMEFT contact terms. We discuss several aspects of bottom-up versus top-down on-shell derivations of the HEFT and SMEFT amplitudes, highlighting in particular the simple counting of HEFT dimensions in the on-shell approach and the transparent relation between perturbative unitarity and gauge-invariance in the little-group covariant massive spinor formalism. Our results provide a formulation of Effective Field Theory analyses directly in terms of observable quantities. For terms with quadratic energy growth, we also provide the mapping to the Warsaw basis." } ], "imprints": [ { "date": "2023-05-31", "publisher": "Springer" } ] }