Meson-baryon bound states in a (2+1)-dimensional strongly coupled lattice QCD model.

Abstract

We consider bound states of a meson and a baryon ~meson and antibaryon! in lattice QCD in a Euclidean formulation. For simplicity, considering the 1 parity sector we analyze an SU(3) theory with a single flavor in 211 dimensions and two-dimensional Dirac matrices. We work in the strong coupling regime, i.e., in a region of parameters such that the hopping parameter k is sufficiently small and k@g0 22, where g0 22 is the pure gauge coupling. There is a meson ~baryon! particle with asymptotic mass 22 lnk (23 lnk) and an isolated dispersion curve. Here, in a ladder approximation, we show that there is no meson baryon ~or meson-antibaryon! bound state solution to the Bethe-Salpeter equation up to the meson-baryon threshold (;25 lnk). The absence of such a bound state is an effect of a spatial range-one repulsive potential that is local in space at order k 3, i.e., the leading order in the hopping parameter k .