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

International audienceWe consider the X(3872) resonance as a JPC=1++ DD¯∗ hadronic molecule. According to heavy quark spin symmetry, there will exist a partner with quantum numbers 2++, X2, which would be a D∗D¯∗ loosely bound state. The X2 is expected to decay dominantly into DD¯, DD¯∗ and D¯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→DD¯∗γ and Xb2→B¯B∗γ decays. These decay modes are more sensitive to the long-distance structure of the resonances and to the DD¯∗ or BB¯∗ final state interaction