We calculate the nucleon resonance contributions to nucleon Compton scattering, including all states with JP=1/2± and JP=3/2± where experimental data for their electromagnetic transition form factors exist. To this end, we construct a tensor basis for the Compton scattering amplitude based on electromagnetic gauge invariance, crossing symmetry and analyticity. The corresponding Compton form factors provide a Lorentz-invariant description of the process in general kinematics, which reduces to the static and generalized polarizabilities in the appropriate kinematic limits. We derive the general forms of the offshell nucleon-to-resonance transition vertices that implement electromagnetic and spin-3/2 gauge invariance, which automatically also defines onshell transition form factors that are free of kinematic constraints. We provide simple fits for those form factors, which we use to analyze the resulting Compton form factors and extract their contributions to the nucleon’s polarizabilities. Apart from the Δ(1232), the resonance contributions to the scalar and spin polarizabilites are very small, although the N(1520) could play a role for the proton’s magnetic polarizability.
{ "_oai": { "updated": "2022-03-04T10:54:38Z", "id": "oai:repo.scoap3.org:43856", "sets": [ "PRD" ] }, "authors": [ { "raw_name": "Gernot Eichmann", "affiliations": [ { "country": "Portugal", "value": "CFTP, Instituto Superior T\u00e9cnico, Universidade de Lisboa, 1049-001 Lisboa, Portugal" } ], "surname": "Eichmann", "given_names": "Gernot", "full_name": "Eichmann, Gernot" }, { "raw_name": "G. Ramalho", "affiliations": [ { "country": "Brazil", "value": "Laborat\u00f3rio de F\u00edsica Te\u00f3rica e Computacional\u2013LFTC, Universidade Cruzeiro do Sul, 01506-000, S\u00e3o Paulo, SP, Brazil" } ], "surname": "Ramalho", "given_names": "G.", "full_name": "Ramalho, G." } ], "titles": [ { "source": "APS", "title": "Nucleon resonances in Compton scattering" } ], "dois": [ { "value": "10.1103/PhysRevD.98.093007" } ], "publication_info": [ { "journal_volume": "98", "journal_title": "Physical Review D", "material": "article", "journal_issue": "9", "year": 2018 } ], "$schema": "http://repo.scoap3.org/schemas/hep.json", "acquisition_source": { "date": "2020-06-29T15:33:08.909377", "source": "APS", "method": "APS", "submission_number": "bca49440b8c511eaad8602163e01809a" }, "page_nr": [ 45 ], "license": [ { "url": "https://creativecommons.org/licenses/by/4.0/", "license": "CC-BY-4.0" } ], "copyright": [ { "statement": "Published by the American Physical Society", "year": "2018" } ], "control_number": "43856", "record_creation_date": "2018-12-03T11:30:16.127813", "_files": [ { "checksum": "md5:8486f60d28be1872b22c5af675417c7b", "filetype": "pdf", "bucket": "523fa381-3c68-4097-9120-571ee99a8991", "version_id": "da3bafbb-4f25-4657-8abd-81d1193e8d45", "key": "10.1103/PhysRevD.98.093007.pdf", "size": 3629585 }, { "checksum": "md5:e52005cd5a7425dd9522446cf825ac9b", "filetype": "xml", "bucket": "523fa381-3c68-4097-9120-571ee99a8991", "version_id": "acdae52f-8e6b-4c7f-b811-631867a5ca61", "key": "10.1103/PhysRevD.98.093007.xml", "size": 1262786 } ], "collections": [ { "primary": "HEP" }, { "primary": "Citeable" }, { "primary": "Published" } ], "arxiv_eprints": [ { "categories": [ "hep-ph", "hep-th", "nucl-th" ], "value": "1806.04579" } ], "abstracts": [ { "source": "APS", "value": "We calculate the nucleon resonance contributions to nucleon Compton scattering, including all states with <math><msup><mi>J</mi><mi>P</mi></msup><mo>=</mo><mn>1</mn><mo>/</mo><msup><mn>2</mn><mo>\u00b1</mo></msup></math> and <math><msup><mi>J</mi><mi>P</mi></msup><mo>=</mo><mn>3</mn><mo>/</mo><msup><mn>2</mn><mo>\u00b1</mo></msup></math> where experimental data for their electromagnetic transition form factors exist. To this end, we construct a tensor basis for the Compton scattering amplitude based on electromagnetic gauge invariance, crossing symmetry and analyticity. The corresponding Compton form factors provide a Lorentz-invariant description of the process in general kinematics, which reduces to the static and generalized polarizabilities in the appropriate kinematic limits. We derive the general forms of the offshell nucleon-to-resonance transition vertices that implement electromagnetic and spin-<math><mn>3</mn><mo>/</mo><mn>2</mn></math> gauge invariance, which automatically also defines onshell transition form factors that are free of kinematic constraints. We provide simple fits for those form factors, which we use to analyze the resulting Compton form factors and extract their contributions to the nucleon\u2019s polarizabilities. Apart from the <math><mi>\u0394</mi><mo>(</mo><mn>1232</mn><mo>)</mo></math>, the resonance contributions to the scalar and spin polarizabilites are very small, although the <math><mi>N</mi><mo>(</mo><mn>1520</mn><mo>)</mo></math> could play a role for the proton\u2019s magnetic polarizability." } ], "imprints": [ { "date": "2018-11-28", "publisher": "APS" } ] }