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

We consider bound states of two baryons (antibaryons) in lattice QCD in a Euclidean formulation. For simplicity, we analyze an SU(3) theory with a single flavor in 2+1 dimensions and two-dimensional Dirac matrices. For a small hopping parameter 0<kappamuch less than1 and large glueball mass, we recently showed the existence of a (anti)baryonlike particle, with an asymptotic mass of the order of -3 ln 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 -5 ln 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 -6 ln kappa.