Prediction of new states from $D^{(\ast )}{B}^{(\ast )}{\bar{B}}^{(\ast )}$ three-body interactions

Abstract

We study three-body systems composed of $D^{(\ast )}$, $B^{(\ast )}$ and ${\bar{B}}^{(\ast )}$ in order to look for possible bound states or resonances. In order to solve the three-body problem, we use the fixed center approach for the Faddeev equations considering that the $B^{\ast }{\bar{B}}^{\ast }(B\bar{B})$ are clusterized systems, generated dynamically, which interact with a third particle $D(D^{\ast })$ whose mass is much smaller than the two-body bound states forming the cluster. In the $D{B}^{\ast }{\bar{B}}^{\ast }$, $D^{\ast }{B}^{\ast }{\bar{B}}^{\ast }$, $DB\bar{B}$ and $D^{\ast }B\bar{B}$ systems with $I=1/2$, we found clear bound state peaks with binding energies typically a few tens MeV and more uncertain broad resonant states about ten MeV above the threshold with widths of a few tens MeV.

7 pages, 2 figures