$D Ξ$ and $D^* Ξ$ Molecular States from One Boson Exchange

Abstract

We explore the existence of $D Ξ$ and $D^* Ξ$ molecular states within the one boson exchange model. We regularize the potential derived in this model with a form factor and a cut-off of the order of $1\,{\rm GeV}$. To determine the cut-off, we use the condition that the $X(3872)$ is reproduced as a pole in the $J^{PC} = 1^{++}$ $D^*\bar{D}$ amplitude. From this we find that the $J^P= {\frac{1}{2}}^{-}$ $D^*\,Ξ$ system is on the verge of binding and has an unnaturally large scattering length. For the $J^P= {\frac{1}{2}}^{-}$ $D\,Ξ$ and the $J^P= {\frac{3}{2}}^{-}$ $D^*\,Ξ$ systems the attraction is not enough to form a bound state. From heavy quark symmetry and the quark model we can extend the previous model to the $P Ξ_{QQ}$ and $P^* Ξ_{QQ}$ systems, with $P = D, \bar{B}$, $P^* = D^*, \bar{B}^*$ and $Ξ_{QQ} = Ξ_{cc}, Ξ_{bb}$. In this case we predict a series of triply heavy pentaquark-like molecules.