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

TL;DR

This paper predicts the existence of $B\bar{B}^*$ bound states based on the properties of the X(3872), heavy quark symmetry, and short-range interactions, including pion exchange effects, with implications for the $Z_b(10610)$ state.

Contribution

It introduces a method to derive $B\bar{B}^*$ bound states from the X(3872) and heavy quark symmetry, incorporating contact interactions and pion exchange.

Findings

Predicted three isoscalar $B\bar{B}^*$ states with specific binding energies.

Estimated the effects of pion exchange on the bound states.

Accommodated the $Z_b(10610)$ within the framework with minor modifications.

Abstract

We discuss the possibility and the description of bound states between $B$ and $\bar{B}^*$ 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 $D\bar{D}^*$ system and (iii) heavy quark symmetry. From these assumptions the binding energy of the possible $B\bar{B}^*$ 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 $^3S_1-{}^3D_1$ state with a binding energy of $20\,{\rm MeV}$ and $6\,{\rm MeV}$ below threshold respectively, and a positive C-parity $^3P_0$ shallow state located almost at the $B\bar{B}^*$ 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.