Decay widths of the spin-2 partners of the X(3872)

Abstract

We consider the $X(3872)$ resonance as a $J^{PC}=1^{++}$ $D{\bar{D}}^{\ast }$ hadronic molecule. According to heavy quark spin symmetry, there will exist a partner with quantum numbers $2^{++}$, $X_2$, which would be a $D^{\ast }{\bar{D}}^{\ast }$ loosely bound state. The $X_2$ is expected to decay dominantly into $D\bar{D}$, $D{\bar{D}}^{\ast }$ and $\bar{D}{D}^{\ast }$ in $d$-wave. In this work, we calculate the decay widths of the $X_2$ resonance into the above channels, as well as those of its bottom partner, $X_{b2}$, the mass of which comes from assuming heavy flavor symmetry for the contact terms. We find partial widths of the $X_2$ and $X_{b2}$ of the order of a few MeV. Finally, we also study the radiative $X_2\to D{\bar{D}}^{\ast }\gamma$ and $X_{b2}\to \bar{B}{B}^{\ast }\gamma$ decays. These decay modes are more sensitive to the long-distance structure of the resonances and to the $D{\bar{D}}^{\ast }$ or $B{\bar{B}}^{\ast }$ final state interaction.

Comments: 46 pages, 11 figures