6533b859fe1ef96bd12b806b

RESEARCH PRODUCT

Binding of the BDD¯ and BDD systems

subject

description

We study theoretically the $BD\overline{D}$ and $BDD$ systems to see if they allow for possible bound or resonant states. The three-body interaction is evaluated implementing the fixed center approximation to the Faddeev equations which considers the interaction of a $D$ or $\overline{D}$ particle with the components of a $BD$ cluster, previously proved to form a bound state. We find an $I({J}^{P})=1/2({0}^{\ensuremath{-}})$ bound state for the $BD\overline{D}$ system at an energy around 8925--8985 MeV within uncertainties, which would correspond to a bottom hidden-charm meson. In contrast, for the $BDD$ system, which would be bottom double-charm and hence manifestly exotic, we have found hints of a bound state in the energy region 8935--8985 MeV, but the results are not stable under the uncertainties of the model, and we cannot assure, nor rule out, the possibility of a $BDD$ three-body state.