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

Abstract

We explore the existence of $D\Xi$ and $D^{\ast }\Xi$ 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 $1\mathrm{GeV}$. To determine the cut-off, we use the condition that the $X(3872)$ is reproduced as a pole in the $J^{PC}=1^{++}$ $D^{\ast }\bar{D}$ amplitude. From this we find that the $J^P={\frac{1}{2}}^{-}$ $D^{\ast }\Xi$ system is on the verge of binding and has an unnaturally large scattering length. For the $J^P={\frac{1}{2}}^{-}$ $D\Xi$ and the $J^P={\frac{3}{2}}^{-}$ $D^{\ast }\Xi$ 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 $P{\Xi }_{QQ}$ and $P^{\ast }{\Xi }_{QQ}$ 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.

Comments: 11 pages, 3 figures, corresponds to published version