Analytic binding energies for two-baryon bound states in 2 + 1 strongly coupled lattice QCD with two-flavors.
Autor(a) principal: | |
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Data de Publicação: | 2013 |
Outros Autores: | , |
Tipo de documento: | Artigo |
Idioma: | eng |
Título da fonte: | Repositório Institucional da UFOP |
Texto Completo: | http://www.repositorio.ufop.br/handle/123456789/8733 https://link.springer.com/article/10.1007/s00220-013-1688-z https://doi.org/10.1007/s00220-013-1688-z |
Resumo: | We consider a lattice SU(3) QCD model in 2 + 1 dimensions, with two flavors and 2 × 2 spin matrices. An imaginary time functional integral formulation with Wilson’s action is used in the strong coupling regime, i.e. small hopping parameter 0 < κ 1, and much smaller plaquette coupling β, 0 < β κ. In this regime, it is known that the low-lying energy-momentum spectrum contains isolated dispersion curves identified with baryons and mesons with asymptotic masses m ≈ −3 ln κ and mm ≈ −2 ln κ, respectively. We prove the existence of two (labelled by ±) two-baryon bound states for each of the total isospin sectors I = 0, 1 and we obtain, in each case, the exact binding energies I ± (of order κ2) which extend to jointly analytic function in κ and β.We also prove that these points are the only mass spectrum up to slightly above the bound state masses. Precisely, we show, for α0 = 1 4, α1 = 1 12, α2 = 1 2, α3 = 34 and small δ > 0, that the bound state masses 2m − I ± are the only points in the mass spectrum in (0, 2m − I ± + δαI κ2), for I = 0, 1, and in (0, 2m − (1 + δ)αI κ2), for I = 2, 3. These results are exact and validate our previous results obtained in a ladder approximation. The method employs suitable two- and four-point correlations with spectral representations and a lattice Bethe-Salpeter equation. For I = 0, 1, a quark, antiquark space-range one potential of order κ2 is found to be the dominant contribution to the two-baryon interaction and the interaction of the individual quark isospins of one baryon with those of the other is described by permanents. A novel spectral free decomposition (but spectral representation motivated, for real κ and β) of the two-point correlation, after performing a complex extension, is a key ingredient in showing the joint analyticity of the binding energy. |
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O’Carroll, MichaelVeiga, Paulo Afonso Faria daFrancisco Neto, Antônio2017-09-18T13:30:27Z2017-09-18T13:30:27Z2013O'CARROL, M.; VEIGA, P. A. F. da; FRANCISCO NETO, A. Analytic binding energies for two-baryon bound states in 2 + 1 strongly coupled lattice QCD with two-flavors. Communications in Mathematical Physics, v. 321, p. 249-282, 2013. Disponível em: <https://link.springer.com/article/10.1007/s00220-013-1688-z>. Acesso em: 20 jul. 2017.1432-0916http://www.repositorio.ufop.br/handle/123456789/8733https://link.springer.com/article/10.1007/s00220-013-1688-zhttps://doi.org/10.1007/s00220-013-1688-zWe consider a lattice SU(3) QCD model in 2 + 1 dimensions, with two flavors and 2 × 2 spin matrices. An imaginary time functional integral formulation with Wilson’s action is used in the strong coupling regime, i.e. small hopping parameter 0 < κ 1, and much smaller plaquette coupling β, 0 < β κ. In this regime, it is known that the low-lying energy-momentum spectrum contains isolated dispersion curves identified with baryons and mesons with asymptotic masses m ≈ −3 ln κ and mm ≈ −2 ln κ, respectively. We prove the existence of two (labelled by ±) two-baryon bound states for each of the total isospin sectors I = 0, 1 and we obtain, in each case, the exact binding energies I ± (of order κ2) which extend to jointly analytic function in κ and β.We also prove that these points are the only mass spectrum up to slightly above the bound state masses. Precisely, we show, for α0 = 1 4, α1 = 1 12, α2 = 1 2, α3 = 34 and small δ > 0, that the bound state masses 2m − I ± are the only points in the mass spectrum in (0, 2m − I ± + δαI κ2), for I = 0, 1, and in (0, 2m − (1 + δ)αI κ2), for I = 2, 3. These results are exact and validate our previous results obtained in a ladder approximation. The method employs suitable two- and four-point correlations with spectral representations and a lattice Bethe-Salpeter equation. For I = 0, 1, a quark, antiquark space-range one potential of order κ2 is found to be the dominant contribution to the two-baryon interaction and the interaction of the individual quark isospins of one baryon with those of the other is described by permanents. A novel spectral free decomposition (but spectral representation motivated, for real κ and β) of the two-point correlation, after performing a complex extension, is a key ingredient in showing the joint analyticity of the binding energy.Analytic binding energies for two-baryon bound states in 2 + 1 strongly coupled lattice QCD with two-flavors.info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleinfo:eu-repo/semantics/openAccessengreponame:Repositório Institucional da UFOPinstname:Universidade Federal de Ouro Preto (UFOP)instacron:UFOPLICENSElicense.txtlicense.txttext/plain; charset=utf-8924http://www.repositorio.ufop.br/bitstream/123456789/8733/2/license.txt62604f8d955274beb56c80ce1ee5dcaeMD52ORIGINALARTIGO_AnalyticBindingEnergies.pdfARTIGO_AnalyticBindingEnergies.pdfapplication/pdf503097http://www.repositorio.ufop.br/bitstream/123456789/8733/1/ARTIGO_AnalyticBindingEnergies.pdf424f9b1b10305a1ce721b2394ccb64daMD51123456789/87332020-01-30 07:39:46.255oai:localhost: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ório InstitucionalPUBhttp://www.repositorio.ufop.br/oai/requestrepositorio@ufop.edu.bropendoar:32332020-01-30T12:39:46Repositório Institucional da UFOP - Universidade Federal de Ouro Preto (UFOP)false |
dc.title.pt_BR.fl_str_mv |
Analytic binding energies for two-baryon bound states in 2 + 1 strongly coupled lattice QCD with two-flavors. |
title |
Analytic binding energies for two-baryon bound states in 2 + 1 strongly coupled lattice QCD with two-flavors. |
spellingShingle |
Analytic binding energies for two-baryon bound states in 2 + 1 strongly coupled lattice QCD with two-flavors. O’Carroll, Michael |
title_short |
Analytic binding energies for two-baryon bound states in 2 + 1 strongly coupled lattice QCD with two-flavors. |
title_full |
Analytic binding energies for two-baryon bound states in 2 + 1 strongly coupled lattice QCD with two-flavors. |
title_fullStr |
Analytic binding energies for two-baryon bound states in 2 + 1 strongly coupled lattice QCD with two-flavors. |
title_full_unstemmed |
Analytic binding energies for two-baryon bound states in 2 + 1 strongly coupled lattice QCD with two-flavors. |
title_sort |
Analytic binding energies for two-baryon bound states in 2 + 1 strongly coupled lattice QCD with two-flavors. |
author |
O’Carroll, Michael |
author_facet |
O’Carroll, Michael Veiga, Paulo Afonso Faria da Francisco Neto, Antônio |
author_role |
author |
author2 |
Veiga, Paulo Afonso Faria da Francisco Neto, Antônio |
author2_role |
author author |
dc.contributor.author.fl_str_mv |
O’Carroll, Michael Veiga, Paulo Afonso Faria da Francisco Neto, Antônio |
description |
We consider a lattice SU(3) QCD model in 2 + 1 dimensions, with two flavors and 2 × 2 spin matrices. An imaginary time functional integral formulation with Wilson’s action is used in the strong coupling regime, i.e. small hopping parameter 0 < κ 1, and much smaller plaquette coupling β, 0 < β κ. In this regime, it is known that the low-lying energy-momentum spectrum contains isolated dispersion curves identified with baryons and mesons with asymptotic masses m ≈ −3 ln κ and mm ≈ −2 ln κ, respectively. We prove the existence of two (labelled by ±) two-baryon bound states for each of the total isospin sectors I = 0, 1 and we obtain, in each case, the exact binding energies I ± (of order κ2) which extend to jointly analytic function in κ and β.We also prove that these points are the only mass spectrum up to slightly above the bound state masses. Precisely, we show, for α0 = 1 4, α1 = 1 12, α2 = 1 2, α3 = 34 and small δ > 0, that the bound state masses 2m − I ± are the only points in the mass spectrum in (0, 2m − I ± + δαI κ2), for I = 0, 1, and in (0, 2m − (1 + δ)αI κ2), for I = 2, 3. These results are exact and validate our previous results obtained in a ladder approximation. The method employs suitable two- and four-point correlations with spectral representations and a lattice Bethe-Salpeter equation. For I = 0, 1, a quark, antiquark space-range one potential of order κ2 is found to be the dominant contribution to the two-baryon interaction and the interaction of the individual quark isospins of one baryon with those of the other is described by permanents. A novel spectral free decomposition (but spectral representation motivated, for real κ and β) of the two-point correlation, after performing a complex extension, is a key ingredient in showing the joint analyticity of the binding energy. |
publishDate |
2013 |
dc.date.issued.fl_str_mv |
2013 |
dc.date.accessioned.fl_str_mv |
2017-09-18T13:30:27Z |
dc.date.available.fl_str_mv |
2017-09-18T13:30:27Z |
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.citation.fl_str_mv |
O'CARROL, M.; VEIGA, P. A. F. da; FRANCISCO NETO, A. Analytic binding energies for two-baryon bound states in 2 + 1 strongly coupled lattice QCD with two-flavors. Communications in Mathematical Physics, v. 321, p. 249-282, 2013. Disponível em: <https://link.springer.com/article/10.1007/s00220-013-1688-z>. Acesso em: 20 jul. 2017. |
dc.identifier.uri.fl_str_mv |
http://www.repositorio.ufop.br/handle/123456789/8733 |
dc.identifier.issn.none.fl_str_mv |
1432-0916 |
dc.identifier.uri2.pt_BR.fl_str_mv |
https://link.springer.com/article/10.1007/s00220-013-1688-z |
dc.identifier.doi.none.fl_str_mv |
https://doi.org/10.1007/s00220-013-1688-z |
identifier_str_mv |
O'CARROL, M.; VEIGA, P. A. F. da; FRANCISCO NETO, A. Analytic binding energies for two-baryon bound states in 2 + 1 strongly coupled lattice QCD with two-flavors. Communications in Mathematical Physics, v. 321, p. 249-282, 2013. Disponível em: <https://link.springer.com/article/10.1007/s00220-013-1688-z>. Acesso em: 20 jul. 2017. 1432-0916 |
url |
http://www.repositorio.ufop.br/handle/123456789/8733 https://link.springer.com/article/10.1007/s00220-013-1688-z https://doi.org/10.1007/s00220-013-1688-z |
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eng |
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