Exact mesonic eightfold way from dynamics and confinement in strongly coupled lattice QCD.

• Autor(a) principal: Francisco Neto, Antônio
• Data de Publicação: 2009
• Outros Autores: O'Carroll, Michael Louis, Veiga, Paulo Afonso Faria da
• Tipo de documento: Artigo
• Idioma: eng
• Título da fonte: Repositório Institucional da UFOP
• Texto Completo: http://www.repositorio.ufop.br/handle/123456789/1947

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.