Baryon-baryon bound states in a(2+1)-dimensional lattice QCD model

Abstract

We consider bound states of two baryons (antibaryons) in lattice QCD in a Euclidean formulation. For simplicity, we analyze an $\mathrm{SU}(3)$ theory with a single flavor in 2+1 dimensions and two-dimensional Dirac matrices. For a small hopping parameter $0<\ensuremath{\kappa}\ensuremath{\ll}1$ and large glueball mass, we recently showed the existence of a (anti)baryonlike particle, with an asymptotic mass of the order of $\ensuremath{-}3\mathrm{ln}\ensuremath{\kappa}$ and with an isolated dispersion curve, i.e., an upper gap property persisting up to near the meson-baryon threshold, which is of order $\ensuremath{-}5\mathrm{ln}\ensuremath{\kappa}.$ Here, we show that there is no baryon-baryon (or antibaryon-antibaryon) bound state solution to the Bethe-Salpeter equation up to the two-baryon threshold, which is approximately $\ensuremath{-}6\mathrm{ln}\ensuremath{\kappa}.$