Study of the $B{\bar{B}}^{\ast }/D{\bar{D}}^{\ast }$ bound states in a Bethe-Salpeter approach

Abstract

In this work the $B{\bar{B}}^{\ast }/D{\bar{D}}^{\ast }$ system is studied in the Bethe-Salpeter approach with quasipotential approximation. In our calculation both direct and cross diagrams are included in the one-boson-exchange potential. The numerical results indicate the existence of a isoscalar bound state $D{\bar{D}}^{\ast }$ with $J^{PC}=1^{++}$, which may be related to the $X(3872)$. In the isovector sector, no bound state is produced from the interactions of $D{\bar{D}}^{\ast }$ and $B{\bar{B}}^{\ast }$, which suggests the molecular state explanations for $Z_b(10610)$ and $Z_c(3900)$ are excluded.

Comments: 6 pages,