Meson-meson bound state in a2+1lattice 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 $\ensuremath{\sim}\ensuremath{-}4\mathrm{ln}\ensuremath{\kappa}$). The corresponding meson masses are equal up to and including $\mathcal{O}({\ensuremath{\kappa}}^{3})$ and are asymptotically of order $\ensuremath{-}2\mathrm{ln}\ensuremath{\kappa}\ensuremath{-}{\ensuremath{\kappa}}^{2}$. 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 $\overline{b}{\ensuremath{\kappa}}^{2}\ensuremath{\simeq}0.02359{\ensuremath{\kappa}}^{2}$. In the context of the strong coupling expansion in $\ensuremath{\kappa}$, 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.