Possible Bound States in the $D^{\ast }{\bar{D}}^{\ast }$/$B^{\ast }{\bar{B}}^{\ast }$ and $D^{\ast }{D}^{\ast }$/${\bar{B}}^{\ast }{\bar{B}}^{\ast }$ Systems within the Bethe-Salpeter Formalism

Abstract

We investigate possible $S$-wave bound states in the $D^{\ast }{\bar{D}}^{\ast }$, $B^{\ast }{\bar{B}}^{\ast }$, $D^{\ast }{D}^{\ast }$, and ${\bar{B}}^{\ast }{\bar{B}}^{\ast }$ systems within the Bethe-Salpeter formalism using one-boson-exchange interactions. Bound state solutions are obtained in the isoscalar hidden-heavy systems with $J^{PC}=0^{++}$, $1^{+-}$, and $2^{++}$, whereas no isovector solutions are found within the parameter range considered. For the doubly heavy systems, solutions are obtained in the allowed $I(J^P)=0(1^{+})$, $1(0^{+})$, and $1(2^{+})$ systems, although the $1(0^{+})$ solution requires a comparatively large cutoff parameter. The bottom systems are bounded more favorably than their charmed counterparts because of their larger reduced masses.