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

We consider the $X(3872)$ resonance as a $J^{PC}=1^{++}$ $Dbar D^*$ hadronic molecule. According to heavy quark spin symmetry, there will exist a partner with quantum numbers $2^{++}$, $X_{2}$, which would be a $D^*bar D^*$ loosely bound state. The $X_{2}$ is expected to decay dominantly into $Dbar D$, $Dbar D^*$ and $bar D D^*$ 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 $X_2to Dbar D^{*}gamma$ and $X_{b2} to bar B B^{*}gamma$ decays. These decay modes are more sensitive to the long-distance structure of the resonances and to the $Dbar D^{*}$ or $Bbar B^{*}$ final state interaction.