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

TL;DR

This study uses the Bethe-Salpeter approach with quasipotential approximation to investigate $Bar{B}^*/Dar{D}^*$ bound states, finding a possible connection to the $X(3872)$ and excluding molecular explanations for certain other states.

Contribution

It introduces a Bethe-Salpeter approach with quasipotential approximation to analyze heavy meson bound states, including both direct and cross diagrams in the potential.

Findings

Identifies a possible isoscalar $Dar{D}^*$ bound state related to $X(3872)

No bound states found in the isovector sector for $Dar{D}^*$ and $Bar{B}^*$

Excludes molecular explanations for $Z_b(10610)$ and $Z_c(3900)$

Abstract

In this work the $B\bar{B}^*/D\bar{D}^*$ 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 $D\bar{D}^*$ 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 $D\bar{D}^*$ and $B\bar{B}^*$, which suggests the molecular state explanations for $Z_b(10610)$ and $Z_c(3900)$ are excluded.