Scattering amplitudes and contour deformations
Autor(a) principal: | |
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Data de Publicação: | 2019 |
Outros Autores: | , , |
Tipo de documento: | Artigo |
Idioma: | eng |
Título da fonte: | Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
Texto Completo: | http://hdl.handle.net/10174/26348 https://doi.org/10.1103/PhysRevD.100.094001 |
Resumo: | We employ a scalar model to exemplify the use of contour deformations when solving Lorentz-invariant integral equations for scattering amplitudes. In particular, we calculate the onshell 2→2 scattering amplitude for the scalar system. The integrals produce branch cuts in the complex plane of the integrand which prohibit a naive Euclidean integration path. By employing contour deformations, we can also access the kinematical regions associated with the scattering amplitude in Minkowski space. We show that in principle a homogeneous Bethe-Salpeter equation, together with analytic continuation methods such as the Resonances-via-Padé method, is sufficient to determine the resonance pole locations on the second Riemann sheet. However, the scalar model investigated here does not produce resonance poles above threshold but instead virtual states on the real axis of the second sheet, which pose difficulties for analytic continuation methods. To address this, we calculate the scattering amplitude on the second sheet directly using the two-body unitarity relation which follows from the scattering equation. |
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Scattering amplitudes and contour deformationsScattering amplitudesBethe-Salpeter equationBound statesNonperturbative effects in quantum field theoryWe employ a scalar model to exemplify the use of contour deformations when solving Lorentz-invariant integral equations for scattering amplitudes. In particular, we calculate the onshell 2→2 scattering amplitude for the scalar system. The integrals produce branch cuts in the complex plane of the integrand which prohibit a naive Euclidean integration path. By employing contour deformations, we can also access the kinematical regions associated with the scattering amplitude in Minkowski space. We show that in principle a homogeneous Bethe-Salpeter equation, together with analytic continuation methods such as the Resonances-via-Padé method, is sufficient to determine the resonance pole locations on the second Riemann sheet. However, the scalar model investigated here does not produce resonance poles above threshold but instead virtual states on the real axis of the second sheet, which pose difficulties for analytic continuation methods. To address this, we calculate the scattering amplitude on the second sheet directly using the two-body unitarity relation which follows from the scattering equation.Fundação para a Ciência e a Tecnologia (FCT)American Physical Society2020-01-09T12:09:17Z2020-01-092019-11-01T00:00:00Zinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articlehttp://hdl.handle.net/10174/26348https://doi.org/10.1103/PhysRevD.100.094001http://hdl.handle.net/10174/26348https://doi.org/10.1103/PhysRevD.100.094001engGernot Eichmann, Pedro Duarte, M. T. Peña, and Alfred Stadler, "Scattering amplitudes and contour deformations", Physical Review D 100, 094001 (2019)ndndndstadler@uevora.pt358Eichmann, GernotDuarte, PedroPeña, M. T.Stadler, Alfredinfo:eu-repo/semantics/openAccessreponame:Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)instname:Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informaçãoinstacron:RCAAP2024-01-03T19:20:58Zoai:dspace.uevora.pt:10174/26348Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-20T01:16:39.344999Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) - Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informaçãofalse |
dc.title.none.fl_str_mv |
Scattering amplitudes and contour deformations |
title |
Scattering amplitudes and contour deformations |
spellingShingle |
Scattering amplitudes and contour deformations Eichmann, Gernot Scattering amplitudes Bethe-Salpeter equation Bound states Nonperturbative effects in quantum field theory |
title_short |
Scattering amplitudes and contour deformations |
title_full |
Scattering amplitudes and contour deformations |
title_fullStr |
Scattering amplitudes and contour deformations |
title_full_unstemmed |
Scattering amplitudes and contour deformations |
title_sort |
Scattering amplitudes and contour deformations |
author |
Eichmann, Gernot |
author_facet |
Eichmann, Gernot Duarte, Pedro Peña, M. T. Stadler, Alfred |
author_role |
author |
author2 |
Duarte, Pedro Peña, M. T. Stadler, Alfred |
author2_role |
author author author |
dc.contributor.author.fl_str_mv |
Eichmann, Gernot Duarte, Pedro Peña, M. T. Stadler, Alfred |
dc.subject.por.fl_str_mv |
Scattering amplitudes Bethe-Salpeter equation Bound states Nonperturbative effects in quantum field theory |
topic |
Scattering amplitudes Bethe-Salpeter equation Bound states Nonperturbative effects in quantum field theory |
description |
We employ a scalar model to exemplify the use of contour deformations when solving Lorentz-invariant integral equations for scattering amplitudes. In particular, we calculate the onshell 2→2 scattering amplitude for the scalar system. The integrals produce branch cuts in the complex plane of the integrand which prohibit a naive Euclidean integration path. By employing contour deformations, we can also access the kinematical regions associated with the scattering amplitude in Minkowski space. We show that in principle a homogeneous Bethe-Salpeter equation, together with analytic continuation methods such as the Resonances-via-Padé method, is sufficient to determine the resonance pole locations on the second Riemann sheet. However, the scalar model investigated here does not produce resonance poles above threshold but instead virtual states on the real axis of the second sheet, which pose difficulties for analytic continuation methods. To address this, we calculate the scattering amplitude on the second sheet directly using the two-body unitarity relation which follows from the scattering equation. |
publishDate |
2019 |
dc.date.none.fl_str_mv |
2019-11-01T00:00:00Z 2020-01-09T12:09:17Z 2020-01-09 |
dc.type.status.fl_str_mv |
info:eu-repo/semantics/publishedVersion |
dc.type.driver.fl_str_mv |
info:eu-repo/semantics/article |
format |
article |
status_str |
publishedVersion |
dc.identifier.uri.fl_str_mv |
http://hdl.handle.net/10174/26348 https://doi.org/10.1103/PhysRevD.100.094001 http://hdl.handle.net/10174/26348 https://doi.org/10.1103/PhysRevD.100.094001 |
url |
http://hdl.handle.net/10174/26348 https://doi.org/10.1103/PhysRevD.100.094001 |
dc.language.iso.fl_str_mv |
eng |
language |
eng |
dc.relation.none.fl_str_mv |
Gernot Eichmann, Pedro Duarte, M. T. Peña, and Alfred Stadler, "Scattering amplitudes and contour deformations", Physical Review D 100, 094001 (2019) nd nd nd stadler@uevora.pt 358 |
dc.rights.driver.fl_str_mv |
info:eu-repo/semantics/openAccess |
eu_rights_str_mv |
openAccess |
dc.publisher.none.fl_str_mv |
American Physical Society |
publisher.none.fl_str_mv |
American Physical Society |
dc.source.none.fl_str_mv |
reponame:Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) instname:Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação instacron:RCAAP |
instname_str |
Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação |
instacron_str |
RCAAP |
institution |
RCAAP |
reponame_str |
Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
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Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
repository.name.fl_str_mv |
Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) - Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação |
repository.mail.fl_str_mv |
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1799136648824356864 |