Deriving the existence of $B{\bar{B}}^{\ast }$ bound states from the X(3872) and Heavy Quark Symmetry

Abstract

We discuss the possibility and the description of bound states between $B$ and ${\bar{B}}^{\ast }$ 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 $D{\bar{D}}^{\ast }$ system and (iii) heavy quark symmetry. From these assumptions the binding energy of the possible $B{\bar{B}}^{\ast }$ 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 ${}^3{S}_1-{}^3{D}_1$ state with a binding energy of $20\mathrm{MeV}$ and $6\mathrm{MeV}$ below threshold respectively, and a positive C-parity ${}^3{P}_0$ shallow state located almost at the $B{\bar{B}}^{\ast }$ threshold. However, large uncertainties are generated as a consequence of the $1/m_Q$ corrections from heavy quark symmetry. Finally, the newly discovered isovector $Z_b(10610)$ state can be easily accommodated within the present framework by a minor modification of the short range dynamics.

Comments: 21 pages, 3 figures; a sign error in the potential has been corrected and new predictions have been computed