Dynamical Eightfold Way in Strongly Coupled Lattice QCD

Abstract

We obtain from the quark-gluon dynamics, the Gell'Mann-Ne'eman eightfold way baryons in an imaginary-time functional integral formulation of 3+1 lattice QCD in the strong coupling regime (small hopping parameter $\kappa>0$). The model has ${\rm SU}(3)_c$ gauge and global ${\rm SU}(3)_f$ flavor symmetries. In the subspace of the physical Hilbert space of vectors with an odd number of quarks, the baryons are associated with isolated dispersion curves in the energy-momentum spectrum. The spin 1/2 octet and spin 3/2 decuplet baryons have asymptotic mass $-3\ln\kappa$ and for each baryon there is an antibaryon with identical spectral properties. All the masses have the form $M=-3\ln\kappa-3\kappa^3/4+\kappa^6 r(\kappa)$, with $r(\kappa)$ real analytic. For each member of the octet $r(\kappa)$ is the same; for each member of the decuplet, $r(0)$ is the same. So, there is no mass splitting within the octet, and within the decuplet up to and including ${\cal O}(\kappa^6)$. However, there is an octet-decuplet mass difference of $3\kappa^6/4+{\cal O}(\kappa^7)$. The baryon and antibaryon spectrum is the only one up to near the meson-baryon threshold of nearly $-5\ln\kappa$. A decoupling of hyperplane method is used to naturally unveil the form of the baryon composite fields (no a priori guesswork), to show the existence of particles and their multiplicities using a spectral representation for the two-baryon correlation. We also obtain the (anti-)baryon dispersion curves which admit the representation $w(\kappa,\vec p)= -3\ln\kappa -3\kappa^3/4+\kappa^3\sum_{j=1,2,3} (1-\cos ^j)/4+r(\kappa,\vec p)$, where $r(\kappa,\vec p)$ is of ${\cal O}(\kappa^6)$.