Meson-meson bound state in a 2 + 1 lattice QCD model with two flavors and strong coupling.

Abstract

We consider the existence of bound states of two mesons in an imaginary-time formulation of lattice QCD. We analyze an SU(3) theory with two flavors in 2 1 dimensions and two-dimensional spin matrices. For a small hopping parameter and a sufficiently large glueball mass, as a preliminary, we show the existence of isoscalar and isovector mesonlike particles that have isolated dispersion curves (upper gap up to near the two-particle threshold 4 ln ). The corresponding meson masses are equal up to and including O 3 and are asymptotically of order 2 ln 2. Considering the zero total isospin sector, we show that there is a meson-meson bound state solution to the Bethe-Salpeter equation in a ladder approximation, below the two-meson threshold, and with binding energy of order b 2 ’ 0:02359 2. In the context of the strong coupling expansion in , we show that there are two sources of meson-meson attraction. One comes from a quark-antiquark exchange. This is not a meson exchange, as the spin indices are not those of the meson particle, and we refer to this as a quasimeson exchange. The other arises from gauge field correlations of four overlapping bonds, two positively oriented and two of opposite orientation. Although the exchange part gives rise to a space range-one attractive potential, the main mechanism for the formation of the bound state comes from the gauge contribution. In our lattice Bethe-Salpeter equation approach, this mechanism is manifested by an attractive distance-zero energy-dependent potential. We recall that no bound state appeared in the one-flavor case, where the repulsive effect of Pauli exclusion is stronger.