Deriving the existence of BB̄∗ bound states from the X(3872) and Heavy Quark Symmetry

We discuss the possibility and the description of bound states between B and B̄∗ mesons. We argue that the existence of such a bound state can be deduced from (i) the weakly bound X(3872) state, (ii) certain assumptions about the short range dynamics of the DD̄∗ system and (iii) heavy quark symmetry. From these assumptions the binding energy of the possible BB̄∗ bound states is determined, first in a theory containing only contact interactions which serves as a straightforward illustration of the method, and then the effects of including the one pion exchange potential are discussed. In this latter case three isoscalar states are predicted: a positive and negative C-parity S1 − D1 state with a binding energy of 20MeV and 6MeV below threshold respectively, and a positive C-parity P0 shallow state located almost at the BB̄ ∗ threshold. However, large uncertainties are generated as a consequence of the 1/mQ corrections from heavy quark symmetry. Finally, the newly discovered isovector Zb(10610) state can be easily accommodated within the present framework by a minor modification of the short range dynamics.