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

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

2011-06-03

arxiv.org/abs/1106.0600v2

Physics

High Energy Physics

High Energy Physics - Phenomenology

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

Scientific paper

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.

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