Exact mesonic eightfold way from dynamics and confinement in strongly coupled lattice QCD.
Autor(a) principal: | |
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Data de Publicação: | 2009 |
Outros Autores: | , |
Tipo de documento: | Artigo |
Idioma: | eng |
Título da fonte: | Repositório Institucional da UFOP |
Texto Completo: | http://www.repositorio.ufop.br/handle/123456789/1947 |
Resumo: | We review our results on the exact determination of the mesonic eightfold way from first principles, directly from the quark-gluon dynamics. For this, we consider an imaginary-time functional integral formulation of 3 + 1 dimensional lattice QCD with Wilson action, three flavors, SU(3)f flavor symmetry and SU(3)c local gauge symmetry. We work in the strong coupling regime: a small hopping parameter κ > 0 and a much smaller plaquette coupling β > 0. By stablishing a Feynman-Kac formula and a spectral representation to the twomeson correlation, we provide a rigorous connection between this correlation and the one-meson energy-momentum spectrum. The particle states can be labeled by the usual SU(3)f quantum numbers of total isospin I and its third-component I3, the quadratic Casimir C2 and, by a partial restoration of the continuous rotational symmetry on the lattice, as well as by the total spin J and its z−component Jz. We show that, up to near the two-meson energy threshold of ≈ −4 lnκ, the spectrum in the meson sector is given only by isolated dispersion curves of the eightfold way mesons. The mesons have all asymptotic mass of −2 lnκ and, by deriving convergent expansions for the masses both in κ and β, we also show a κ4 mass splitting between the J = 0, 1 states. The splitting persists for β _= 0. Our approach employs the decoupling of hyperplane method to uncover the basic excitations, complex analysis to determine the dispersion curves and a correlation subtraction method to show the curves are isolated. Using the latter and recalling our similar results for baryons, we also show confinement up to near the two-meson threshold. |
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Francisco Neto, AntônioO'Carroll, Michael LouisVeiga, Paulo Afonso Faria da2012-12-03T14:07:46Z2012-12-03T14:07:46Z2009FRANCISCO NETO, A.; O'CARROLL, M. L.; VEIGA, P. A. F. da. Exact mesonic eightfold way from dynamics and confinement in strongly coupled lattice QCD. Nuclear Physics B (Proc. Suppl.) v. 186, n. 1, p. 117–120, 2009. Disponível em: <https://www.sciencedirect.com/science/article/pii/S0920563208004908>. Acesso em: 30 nov. 201205503213http://www.repositorio.ufop.br/handle/123456789/1947We review our results on the exact determination of the mesonic eightfold way from first principles, directly from the quark-gluon dynamics. For this, we consider an imaginary-time functional integral formulation of 3 + 1 dimensional lattice QCD with Wilson action, three flavors, SU(3)f flavor symmetry and SU(3)c local gauge symmetry. We work in the strong coupling regime: a small hopping parameter κ > 0 and a much smaller plaquette coupling β > 0. By stablishing a Feynman-Kac formula and a spectral representation to the twomeson correlation, we provide a rigorous connection between this correlation and the one-meson energy-momentum spectrum. The particle states can be labeled by the usual SU(3)f quantum numbers of total isospin I and its third-component I3, the quadratic Casimir C2 and, by a partial restoration of the continuous rotational symmetry on the lattice, as well as by the total spin J and its z−component Jz. We show that, up to near the two-meson energy threshold of ≈ −4 lnκ, the spectrum in the meson sector is given only by isolated dispersion curves of the eightfold way mesons. The mesons have all asymptotic mass of −2 lnκ and, by deriving convergent expansions for the masses both in κ and β, we also show a κ4 mass splitting between the J = 0, 1 states. The splitting persists for β _= 0. Our approach employs the decoupling of hyperplane method to uncover the basic excitations, complex analysis to determine the dispersion curves and a correlation subtraction method to show the curves are isolated. Using the latter and recalling our similar results for baryons, we also show confinement up to near the two-meson threshold.Exact mesonic eightfold way from dynamics and confinement in strongly coupled lattice QCD.info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleO periódico Nuclear Physics B concede permissão para depósito do artigo no Repositório Institucional da UFOP. Número da licença: 3292420250116.info:eu-repo/semantics/openAccessengreponame:Repositório Institucional da UFOPinstname:Universidade Federal de Ouro Preto (UFOP)instacron:UFOPLICENSElicense.txtlicense.txttext/plain; charset=utf-81748http://www.repositorio.ufop.br/bitstream/123456789/1947/2/license.txt8a4605be74aa9ea9d79846c1fba20a33MD52ORIGINALARTIGO_ExactMesonicEightfold.pdfARTIGO_ExactMesonicEightfold.pdfapplication/pdf210231http://www.repositorio.ufop.br/bitstream/123456789/1947/1/ARTIGO_ExactMesonicEightfold.pdf0ec4a1a50d44528879dc499ef629ea10MD51123456789/19472019-03-15 12:30:02.116oai:localhost: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Repositório InstitucionalPUBhttp://www.repositorio.ufop.br/oai/requestrepositorio@ufop.edu.bropendoar:32332019-03-15T16:30:02Repositório Institucional da UFOP - Universidade Federal de Ouro Preto (UFOP)false |
dc.title.pt_BR.fl_str_mv |
Exact mesonic eightfold way from dynamics and confinement in strongly coupled lattice QCD. |
title |
Exact mesonic eightfold way from dynamics and confinement in strongly coupled lattice QCD. |
spellingShingle |
Exact mesonic eightfold way from dynamics and confinement in strongly coupled lattice QCD. Francisco Neto, Antônio |
title_short |
Exact mesonic eightfold way from dynamics and confinement in strongly coupled lattice QCD. |
title_full |
Exact mesonic eightfold way from dynamics and confinement in strongly coupled lattice QCD. |
title_fullStr |
Exact mesonic eightfold way from dynamics and confinement in strongly coupled lattice QCD. |
title_full_unstemmed |
Exact mesonic eightfold way from dynamics and confinement in strongly coupled lattice QCD. |
title_sort |
Exact mesonic eightfold way from dynamics and confinement in strongly coupled lattice QCD. |
author |
Francisco Neto, Antônio |
author_facet |
Francisco Neto, Antônio O'Carroll, Michael Louis Veiga, Paulo Afonso Faria da |
author_role |
author |
author2 |
O'Carroll, Michael Louis Veiga, Paulo Afonso Faria da |
author2_role |
author author |
dc.contributor.author.fl_str_mv |
Francisco Neto, Antônio O'Carroll, Michael Louis Veiga, Paulo Afonso Faria da |
description |
We review our results on the exact determination of the mesonic eightfold way from first principles, directly from the quark-gluon dynamics. For this, we consider an imaginary-time functional integral formulation of 3 + 1 dimensional lattice QCD with Wilson action, three flavors, SU(3)f flavor symmetry and SU(3)c local gauge symmetry. We work in the strong coupling regime: a small hopping parameter κ > 0 and a much smaller plaquette coupling β > 0. By stablishing a Feynman-Kac formula and a spectral representation to the twomeson correlation, we provide a rigorous connection between this correlation and the one-meson energy-momentum spectrum. The particle states can be labeled by the usual SU(3)f quantum numbers of total isospin I and its third-component I3, the quadratic Casimir C2 and, by a partial restoration of the continuous rotational symmetry on the lattice, as well as by the total spin J and its z−component Jz. We show that, up to near the two-meson energy threshold of ≈ −4 lnκ, the spectrum in the meson sector is given only by isolated dispersion curves of the eightfold way mesons. The mesons have all asymptotic mass of −2 lnκ and, by deriving convergent expansions for the masses both in κ and β, we also show a κ4 mass splitting between the J = 0, 1 states. The splitting persists for β _= 0. Our approach employs the decoupling of hyperplane method to uncover the basic excitations, complex analysis to determine the dispersion curves and a correlation subtraction method to show the curves are isolated. Using the latter and recalling our similar results for baryons, we also show confinement up to near the two-meson threshold. |
publishDate |
2009 |
dc.date.issued.fl_str_mv |
2009 |
dc.date.accessioned.fl_str_mv |
2012-12-03T14:07:46Z |
dc.date.available.fl_str_mv |
2012-12-03T14:07:46Z |
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 |
FRANCISCO NETO, A.; O'CARROLL, M. L.; VEIGA, P. A. F. da. Exact mesonic eightfold way from dynamics and confinement in strongly coupled lattice QCD. Nuclear Physics B (Proc. Suppl.) v. 186, n. 1, p. 117–120, 2009. Disponível em: <https://www.sciencedirect.com/science/article/pii/S0920563208004908>. Acesso em: 30 nov. 2012 |
dc.identifier.uri.fl_str_mv |
http://www.repositorio.ufop.br/handle/123456789/1947 |
dc.identifier.issn.none.fl_str_mv |
05503213 |
identifier_str_mv |
FRANCISCO NETO, A.; O'CARROLL, M. L.; VEIGA, P. A. F. da. Exact mesonic eightfold way from dynamics and confinement in strongly coupled lattice QCD. Nuclear Physics B (Proc. Suppl.) v. 186, n. 1, p. 117–120, 2009. Disponível em: <https://www.sciencedirect.com/science/article/pii/S0920563208004908>. Acesso em: 30 nov. 2012 05503213 |
url |
http://www.repositorio.ufop.br/handle/123456789/1947 |
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eng |
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eng |
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