The recoil correction and spin-orbit force for the possible $B^{\ast }{\bar{B}}^{\ast }$ and $D^{\ast }{\bar{D}}^{\ast }$ states

Abstract

In the framework of the one-boson exchange model, we have calculated the effective potentials between two heavy mesons $B^{\ast }{\bar{B}}^{\ast }$ and $D^{\ast }{\bar{D}}^{\ast }$ from the t- and u-channel $\pi$-, $\eta$-, $\rho$-, $\omega$- and $\sigma$-meson exchanges. We keep the recoil corrections to the $B^{\ast }{\bar{B}}^{\ast }$ and $D^{\ast }{\bar{D}}^{\ast }$ systems up to $O(\frac{1}{M^2})$, which turns out to be important for the very loosely bound molecular states. Our numerical results show that the momentum-related corrections are favorable to the formation of the molecular states in the $I^G=1^{+}$, $J^{PC}=1^{+-}$ in the $B^{\ast }{\bar{B}}^{\ast }$ and $D^{\ast }{\bar{D}}^{\ast }$ systems.

Comments: 12 pages, 9 figures. arXiv admin note: substantial text overlap with arXiv:1403.4043