$D\mathrm{\Xi }$ and $D^{\ast }\mathrm{\Xi }$ Molecular States from One Boson Exchange

We explore the existence of $D\mathrm{\Xi }$ and $D^{\ast }\mathrm{\Xi }$ 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 $1\mathrm{G}\mathrm{e}\mathrm{V}$. To determine the cut-off, we use the condition that the $X(3872)$ is reproduced as a pole in the $J^{PC}=1^{++}$ $D^{\ast }\bar{D}$ amplitude. From this we find that the $J^P= {\frac{1}{2}}^{-}$ $D^{\ast }\mathrm{\Xi }$ system is on the verge of binding and has an unnaturally large scattering length. For the $J^P={\frac{1}{2}}^{-}$ $D\mathrm{\Xi }$ and the $J^P={\frac{3}{2}}^{-}$ $D^{\ast }\mathrm{\Xi }$ 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 $P{\mathrm{\Xi }}_{QQ}$ and $P^{\ast }{\mathrm{\Xi }}_{QQ}$ systems, with $P=D,\bar{B}$, $P^{\ast }=D^{\ast },{\bar{B}}^{\ast }$ and $\Xi_{QQ} = \Xi_{cc}, \Xi_{bb}$. In this case we predict a series of triply heavy pentaquark-like molecules.