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

We consider the X(3872) resonance as a J^PC=1⁺⁺ DD̄^* hadronic molecule. According to heavy quark spin symmetry, there will exist a partner with quantum numbers 2⁺⁺ , X₂ , which would be a D^*D̄^* loosely bound state. The X₂ is expected to decay dominantly into DD̄ , DD̄^* and D̄ D^* in d-wave. In this work, we calculate the decay widths of the X₂ resonance into the above channels, as well as those of its bottom partner, Xb2 , the mass of which comes from assuming heavy flavor symmetry for the contact terms. We find partial widths of the X₂ and Xb2 of the order of a few MeV. Finally, we also study the radiative X₂→ DD̄*γ and Xb2 → B̄ B*γ decays. These decay modes are more sensitive to the long-distance structure of the resonances and to the DD̄* or BB̄* final state interaction.