Heavy-quark spin and flavor symmetry partners of the X (3872) revisited: What can we learn from the one boson exchange model?

Heavy-quark symmetry as applied to heavy hadron systems implies that their interactions are independent of their heavy-quark spin (heavy-quark spin symmetry) and heavy flavor contents (heavy flavor symmetry). In the molecular hypothesis the X(3872) resonance is a 1++ D∗D bound state. If this is the case, the application of heavy-quark symmetry to a molecular X(3872) suggests the existence of a series of partner states, the most obvious of which is a possible 2++ D∗D∗ bound state for which the two-body potential is identical to that of the 1++ D∗D system, the reason being that these two heavy hadron-antihadron states have identical light-spin content. As already discussed in the literature, this leads to the prediction of a partner state at 4012 MeV, at least in the absence of other dynamical effects which might affect the location of this molecule. However the prediction of further heavy-quark symmetry partners cannot be made solely on the basis of symmetry and requires additional information. We propose to use the one-boson-exchange model to fill this gap, in which case we will be able to predict or discard the existence of other partner states. Besides the isoscalar 2++ D∗D∗ bound state, we correctly reproduce the location and quantum numbers of the isovector hidden-bottom Zb(10610) and Zb(10650) molecular candidates. We also predict the hidden-bottom 1++ B∗B∗ and 2++ B∗B∗ partners of the X(3872), in agreement with previous theoretical speculations, plus a series of other states. The isoscalar, doubly charmed 1+ DD∗ and D∗D∗ molecules, and their doubly bottomed counterparts are likely to bind, providing a few instances of explicitly exotic systems.