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

Abstract

We consider bound states of two mesons ~antimesons! in lattice quantum chromodynamics in an Euclidean formulation. For simplicity, we analyze an SU~3! theory with a single flavor in 211 dimensions and twodimensional Dirac matrices. For a small hopping parameter k and small plaquette coupling g0 22, such that 0 ,g0 22!k!1, recently we showed the existence of a ~anti!mesonlike particle, with an asymptotic mass of the order of 22 lnk and with an isolated dispersion curve—i.e., an upper gap property persisting up to near the meson-meson threshold which is of the order of 24 lnk. Here, in a ladder approximation, we show that there is no meson-meson ~or antimeson-antimeson! bound state solution to the Bethe-Salpeter equation up to the two-meson threshold. Remarkably the absence of such a bound state is an effect of a potential which is nonlocal in space at order k 2, i.e., the leading order in the hopping parameter k. A local potential appears only at order k 4 and is repulsive. The relevant spectral properties for our model are unveiled by considering the correspondence between the lattice Bethe-Salpeter equation and a lattice Schro¨dinger resolvent equation with a nonlocal potential.