$D\mathrm{\Xi }$ and $D^{*}\mathrm{\Xi }$ molecular states from one boson exchange

We explore the existence of $D\mathrm{\Xi }$ and $D^{*}\mathrm{\Xi }$ molecular states within the one boson exchange model. We regularize the potential derived in this model with a form factor and a cutoff of the order of 1 GeV. To determine the cutoff, we use the condition that the $X(3872)$ is reproduced as a pole in the $J^{PC}=1^{++}$ $D^{*}\overline{D}$ amplitude. From this, we find that the $J^P={\frac{1}{2}}^{-}$ $D^{*}\mathrm{\Xi }$ 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 $J^P={\frac{3}{2}}^{-}$ $D^{*}\mathrm{\Xi }$ 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 $P^{*}{\mathrm{\Xi }}_{QQ}$ systems, with $P=B$, $D$ and ${\mathrm{\Xi }}_{QQ}={\mathrm{\Xi }}_{cc},{\mathrm{\Xi }}_{bb}$. In this case, we predict a series of triply heavy pentaquarklike molecules.

Figure 1

Binding energies (red line) and root-mean-square radii (black line) for the $D\mathrm{\Xi }$ and $D^{*}\mathrm{\Xi }$ molecules depending on the reduced mass. The upper, middle, and lower panels correspond to the ${\frac{1}{2}}^{-}D\mathrm{\Xi }/D{\mathrm{\Xi }}_{QQ}$, ${\frac{1}{2}}^{-}$ $D^{*}\mathrm{\Xi }/D^{*}{\mathrm{\Xi }}_{QQ}$, and ${\frac{3}{2}}^{-}$ $D^{*}\mathrm{\Xi }/D^{*}{\mathrm{\Xi }}_{QQ}$ molecules, respectively. The vertical dotted lines indicate the reduced masses of the different molecules considered. The calculations are made with a form factor cutoff $\mathrm{\Lambda }={\mathrm{\Lambda }}_X=1.04\mathrm{GeV}$, which corresponds to the cutoff for which the $X(3872)$ is reproduced in the OBE model we use.