Born-Oppenheimer approximation in an effective field theory language
Autor(a) principal: | |
---|---|
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/11449/228500 |
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 H2+ diatomic molecule that are relevant to compute its spectrum up to O(mα5). 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. |
id |
UNSP_b7daf25416274644f1ce2a15d1503ae1 |
---|---|
oai_identifier_str |
oai:repositorio.unesp.br:11449/228500 |
network_acronym_str |
UNSP |
network_name_str |
Repositório Institucional da UNESP |
repository_id_str |
2946 |
spelling |
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 H2+ diatomic molecule that are relevant to compute its spectrum up to O(mα5). 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.Physik-Department Technische Universität München, James-Franck-Strasse 1Institute for Advanced Study Technische Universität München, Lichtenbergstrasse 2aInstituto de Física Teórica Universidade Estadual Paulista, Rua Dr. Bento Teobaldo Ferraz, 271 - Bloco IIInstituto de Física Teórica Universidade Estadual Paulista, Rua Dr. Bento Teobaldo Ferraz, 271 - Bloco IITechnische Universität MünchenUniversidade Estadual Paulista (UNESP)Brambilla, NoraKrein, Gastão [UNESP]Tarrús Castellà, JaumeVairo, Antonio2022-04-29T08:27:00Z2022-04-29T08:27:00Z2018-01-01info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articlehttp://dx.doi.org/10.1103/PhysRevD.97.016016Physical Review D, v. 97, n. 1, 2018.2470-00292470-0010http://hdl.handle.net/11449/22850010.1103/PhysRevD.97.0160162-s2.0-85041714561Scopusreponame:Repositório Institucional da UNESPinstname:Universidade Estadual Paulista (UNESP)instacron:UNESPengPhysical Review Dinfo:eu-repo/semantics/openAccess2022-04-29T08:27:00Zoai:repositorio.unesp.br:11449/228500Repositório InstitucionalPUBhttp://repositorio.unesp.br/oai/requestopendoar:29462022-04-29T08:27Repositório 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, Gastão [UNESP] Tarrús Castellà, Jaume Vairo, Antonio |
author_role |
author |
author2 |
Krein, Gastão [UNESP] Tarrús Castellà, Jaume Vairo, Antonio |
author2_role |
author author author |
dc.contributor.none.fl_str_mv |
Technische Universität München Universidade Estadual Paulista (UNESP) |
dc.contributor.author.fl_str_mv |
Brambilla, Nora Krein, Gastão [UNESP] Tarrús Castellà, Jaume 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 H2+ diatomic molecule that are relevant to compute its spectrum up to O(mα5). 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 |
2018-01-01 2022-04-29T08:27:00Z 2022-04-29T08:27:00Z |
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, v. 97, n. 1, 2018. 2470-0029 2470-0010 http://hdl.handle.net/11449/228500 10.1103/PhysRevD.97.016016 2-s2.0-85041714561 |
url |
http://dx.doi.org/10.1103/PhysRevD.97.016016 http://hdl.handle.net/11449/228500 |
identifier_str_mv |
Physical Review D, v. 97, n. 1, 2018. 2470-0029 2470-0010 10.1103/PhysRevD.97.016016 2-s2.0-85041714561 |
dc.language.iso.fl_str_mv |
eng |
language |
eng |
dc.relation.none.fl_str_mv |
Physical Review D |
dc.rights.driver.fl_str_mv |
info:eu-repo/semantics/openAccess |
eu_rights_str_mv |
openAccess |
dc.source.none.fl_str_mv |
Scopus 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 |
|
_version_ |
1799965113023725568 |