BB intermeson potentials in the quark model - art. no. 045202

In this paper we derive quark model results for scattering amplitudes and e quivalent low energy potentials for heavy meson pairs, in which each meson contains a heavy quark. This "BB" system is an attractive theoretical labor atory for the study of the nuclear force between color singlets; the hadron ic system is relatively simple, and there are lattice gauge theory (LGT) re sults for V-BB(r) which may be compared to phenomenological models. We find that the quark model potential (after lattice smearing) has qualitative si milarities to the LGT potential in the two B*B* channels in which direct co mparison 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 and I = 1 potentials also appears similar to LGT results at intermed iate r. There may however be a discrepancy between the LGT and quark model I = 1 BE potentials. A numerical study of the two-meson Schrodinger equatio ns in the (<b(q)over bar>)(b<b(q)over bar>) and (<c(q)over bar>)(<c(q)over bar>) sectors with the quark model potentials finds a single BB "molecule," in the I = 0 BB* sector. Binding in other channels might occur if the quar k model forces are augmented by pion exchange. [S0556-2813(99)03409-3].