In this paper we derive quark model results for scattering amplitudes and equivalent low energy potentials for heavy meson pairs, in which each meson contains a heavy quark. This “BB” system is an attractive theoretical laboratory for the study of the nuclear force between color singlets; the hadronic system is relatively simple, and there are lattice gauge theory (LGT) results for $V_{\mathrm{BB}}\mathrm{}\left(r\right)\mathrm{}$ which may be compared to phenomenological models. We find that the quark model potential (after lattice smearing) has qualitative similarities to the LGT potential in the two $B^{*}{B}^{*}$ channels in which direct comparison is possible, although there is evidence of a difference in length scales. The quark model prediction of equal magnitude but opposite sign for $I=0\mathrm{}$ and $I=1\mathrm{}$ potentials also appears similar to LGT results at intermediate r. There may however be a discrepancy between the LGT and quark model $I=1\mathrm{}$ $\mathrm{BB}$ potentials. A numerical study of the two-meson Schrödinger equations in the $\left(b\overline{q}\right)\left(b\overline{q}\right)$ and $\left(c\overline{q}\right)\left(c\overline{q}\right)$ sectors with the quark model potentials finds a single BB “molecule,” in the $I=0\mathrm{}$ ${\mathrm{BB}}^{*}$ sector. Binding in other channels might occur if the quark model forces are augmented by pion exchange.

• Received 1 March 1999

DOI:https://doi.org/10.1103/PhysRevC.60.045202