Born-Oppenheimer approximation in an effective field theory language
Autor(a) principal: | |
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Data de Publicação: | 2018 |
Outros Autores: | , , |
Tipo de documento: | Artigo |
Idioma: | eng |
Título da fonte: | Repositório Institucional da UNESP |
Texto Completo: | http://dx.doi.org/10.1103/PhysRevD.97.016016 http://hdl.handle.net/11449/163770 |
Resumo: | The Born-Oppenheimer approximation is the standard tool for the study of molecular systems. It is founded on the observation that the energy scale of the electron dynamics in a molecule is larger than that of the nuclei. A very similar physical picture can be used to describe QCD states containing heavy quarks as well as light-quarks or gluonic excitations. In this work, we derive the Born-Oppenheimer approximation for QED molecular systems in an effective field theory framework by sequentially integrating out degrees of freedom living at energies above the typical energy scale where the dynamics of the heavy degrees of freedom occurs. In particular, we compute the matching coefficients of the effective field theory for the case of the H-2(+) diatomic molecule that are relevant to compute its spectrum up to O(m alpha(5)) thorn. Ultrasoft photon loops contribute at this order, being ultimately responsible for the molecular Lamb shift. In the effective field theory the scaling of all the operators is homogeneous, which facilitates the determination of all the relevant contributions, an observation that may become useful for high-precision calculations. Using the above case as a guidance, we construct under some conditions an effective field theory for QCD states formed by a color-octet heavy quark-antiquark pair bound with a color-octet light-quark pair or excited gluonic state, highlighting the similarities and differences between the QED and QCD systems. Assuming that the multipole expansion is applicable, we construct the heavy-quark potential up to next-to-leading order in the multipole expansion in terms of nonperturbative matching coefficients to be obtained from lattice QCD. |
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Born-Oppenheimer approximation in an effective field theory languageThe Born-Oppenheimer approximation is the standard tool for the study of molecular systems. It is founded on the observation that the energy scale of the electron dynamics in a molecule is larger than that of the nuclei. A very similar physical picture can be used to describe QCD states containing heavy quarks as well as light-quarks or gluonic excitations. In this work, we derive the Born-Oppenheimer approximation for QED molecular systems in an effective field theory framework by sequentially integrating out degrees of freedom living at energies above the typical energy scale where the dynamics of the heavy degrees of freedom occurs. In particular, we compute the matching coefficients of the effective field theory for the case of the H-2(+) diatomic molecule that are relevant to compute its spectrum up to O(m alpha(5)) thorn. Ultrasoft photon loops contribute at this order, being ultimately responsible for the molecular Lamb shift. In the effective field theory the scaling of all the operators is homogeneous, which facilitates the determination of all the relevant contributions, an observation that may become useful for high-precision calculations. Using the above case as a guidance, we construct under some conditions an effective field theory for QCD states formed by a color-octet heavy quark-antiquark pair bound with a color-octet light-quark pair or excited gluonic state, highlighting the similarities and differences between the QED and QCD systems. Assuming that the multipole expansion is applicable, we construct the heavy-quark potential up to next-to-leading order in the multipole expansion in terms of nonperturbative matching coefficients to be obtained from lattice QCD.DFGNSFCDFG cluster of excellence Origin and Structure of the UniverseBayerische Hochschulzentrum fur Lateinamerika (BAYLAT) of the Bayerischen Staatsministeriums fur Bildung und Kultus, Wissenschaft und Kunst (StMBW)Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)Bavarian State Ministry of Education, Science and the Arts through the TUM International Center Visiting ProgramConselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)Tech Univ Munich, Phys Dept, James Franck Str 1, D-85748 Garching, GermanyTech Univ Munich, Inst Adv Study, Lichtenbergstr 2a, D-85748 Garching, GermanyUniv Estadual Paulista, Inst Fis Teor, Rua Dr Bento Teobaldo Ferraz,271 Bloco 2, BR-01140070 Sao Paulo, SP, BrazilUniv Estadual Paulista, Inst Fis Teor, Rua Dr Bento Teobaldo Ferraz,271 Bloco 2, BR-01140070 Sao Paulo, SP, BrazilBayerische Hochschulzentrum fur Lateinamerika (BAYLAT) of the Bayerischen Staatsministeriums fur Bildung und Kultus, Wissenschaft und Kunst (StMBW): 914-20.1.3Bayerische Hochschulzentrum fur Lateinamerika (BAYLAT) of the Bayerischen Staatsministeriums fur Bildung und Kultus, Wissenschaft und Kunst (StMBW): 2013/50841-1FAPESP: 914-20.1.3FAPESP: 2013/50841-1CNPq: 305894/2009-9FAPESP: 2013/01907-0Amer Physical SocTech Univ MunichUniversidade Estadual Paulista (Unesp)Brambilla, NoraKrein, Gastao [UNESP]Castella, Jaume TarrusVairo, Antonio2018-11-26T17:44:55Z2018-11-26T17:44:55Z2018-01-25info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/article16application/pdfhttp://dx.doi.org/10.1103/PhysRevD.97.016016Physical Review D. College Pk: Amer Physical Soc, v. 97, n. 1, 16 p., 2018.2470-0010http://hdl.handle.net/11449/16377010.1103/PhysRevD.97.016016WOS:000423429400018WOS000423429400018.pdfWeb of Sciencereponame:Repositório Institucional da UNESPinstname:Universidade Estadual Paulista (UNESP)instacron:UNESPengPhysical Review D1,801info:eu-repo/semantics/openAccess2023-12-28T06:15:40Zoai:repositorio.unesp.br:11449/163770Repositório InstitucionalPUBhttp://repositorio.unesp.br/oai/requestopendoar:29462023-12-28T06:15:40Repositório Institucional da UNESP - Universidade Estadual Paulista (UNESP)false |
dc.title.none.fl_str_mv |
Born-Oppenheimer approximation in an effective field theory language |
title |
Born-Oppenheimer approximation in an effective field theory language |
spellingShingle |
Born-Oppenheimer approximation in an effective field theory language Brambilla, Nora |
title_short |
Born-Oppenheimer approximation in an effective field theory language |
title_full |
Born-Oppenheimer approximation in an effective field theory language |
title_fullStr |
Born-Oppenheimer approximation in an effective field theory language |
title_full_unstemmed |
Born-Oppenheimer approximation in an effective field theory language |
title_sort |
Born-Oppenheimer approximation in an effective field theory language |
author |
Brambilla, Nora |
author_facet |
Brambilla, Nora Krein, Gastao [UNESP] Castella, Jaume Tarrus Vairo, Antonio |
author_role |
author |
author2 |
Krein, Gastao [UNESP] Castella, Jaume Tarrus Vairo, Antonio |
author2_role |
author author author |
dc.contributor.none.fl_str_mv |
Tech Univ Munich Universidade Estadual Paulista (Unesp) |
dc.contributor.author.fl_str_mv |
Brambilla, Nora Krein, Gastao [UNESP] Castella, Jaume Tarrus Vairo, Antonio |
description |
The Born-Oppenheimer approximation is the standard tool for the study of molecular systems. It is founded on the observation that the energy scale of the electron dynamics in a molecule is larger than that of the nuclei. A very similar physical picture can be used to describe QCD states containing heavy quarks as well as light-quarks or gluonic excitations. In this work, we derive the Born-Oppenheimer approximation for QED molecular systems in an effective field theory framework by sequentially integrating out degrees of freedom living at energies above the typical energy scale where the dynamics of the heavy degrees of freedom occurs. In particular, we compute the matching coefficients of the effective field theory for the case of the H-2(+) diatomic molecule that are relevant to compute its spectrum up to O(m alpha(5)) thorn. Ultrasoft photon loops contribute at this order, being ultimately responsible for the molecular Lamb shift. In the effective field theory the scaling of all the operators is homogeneous, which facilitates the determination of all the relevant contributions, an observation that may become useful for high-precision calculations. Using the above case as a guidance, we construct under some conditions an effective field theory for QCD states formed by a color-octet heavy quark-antiquark pair bound with a color-octet light-quark pair or excited gluonic state, highlighting the similarities and differences between the QED and QCD systems. Assuming that the multipole expansion is applicable, we construct the heavy-quark potential up to next-to-leading order in the multipole expansion in terms of nonperturbative matching coefficients to be obtained from lattice QCD. |
publishDate |
2018 |
dc.date.none.fl_str_mv |
2018-11-26T17:44:55Z 2018-11-26T17:44:55Z 2018-01-25 |
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://dx.doi.org/10.1103/PhysRevD.97.016016 Physical Review D. College Pk: Amer Physical Soc, v. 97, n. 1, 16 p., 2018. 2470-0010 http://hdl.handle.net/11449/163770 10.1103/PhysRevD.97.016016 WOS:000423429400018 WOS000423429400018.pdf |
url |
http://dx.doi.org/10.1103/PhysRevD.97.016016 http://hdl.handle.net/11449/163770 |
identifier_str_mv |
Physical Review D. College Pk: Amer Physical Soc, v. 97, n. 1, 16 p., 2018. 2470-0010 10.1103/PhysRevD.97.016016 WOS:000423429400018 WOS000423429400018.pdf |
dc.language.iso.fl_str_mv |
eng |
language |
eng |
dc.relation.none.fl_str_mv |
Physical Review D 1,801 |
dc.rights.driver.fl_str_mv |
info:eu-repo/semantics/openAccess |
eu_rights_str_mv |
openAccess |
dc.format.none.fl_str_mv |
16 application/pdf |
dc.publisher.none.fl_str_mv |
Amer Physical Soc |
publisher.none.fl_str_mv |
Amer Physical Soc |
dc.source.none.fl_str_mv |
Web of Science reponame:Repositório Institucional da UNESP instname:Universidade Estadual Paulista (UNESP) instacron:UNESP |
instname_str |
Universidade Estadual Paulista (UNESP) |
instacron_str |
UNESP |
institution |
UNESP |
reponame_str |
Repositório Institucional da UNESP |
collection |
Repositório Institucional da UNESP |
repository.name.fl_str_mv |
Repositório Institucional da UNESP - Universidade Estadual Paulista (UNESP) |
repository.mail.fl_str_mv |
|
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1799965431964893184 |