The Spin-orbit force, recoil corrections and possible $B{\bar{B}}^{\ast }$ and $D{\bar{D}}^{\ast }$ molecular states

Abstract

In the framework of the one boson exchange model, we have calculated the effective potentials between two heavy mesons $B{\bar{B}}^{\ast }$ and $D{\bar{D}}^{\ast }$ from the t- and u-channel $\pi$, $\eta$, $\rho$, $\omega$ and $\sigma$ meson exchange with four kinds of quantum number: $I=0$, $J^{PC}=1^{++}$; $I=0$, $J^{PC}=1^{+-}$; $I=1$, $J^{PC}=1^{++}$; $I=1$, $J^{PC}=1^{+-}$. We keep the recoil corrections to the $B{\bar{B}}^{\ast }$ and $D{\bar{D}}^{\ast }$ system up to $O(\frac{1}{M^2})$. The spin orbit force appears at $O(\frac{1}{M})$, which turns out to be important for the very loosely bound molecular states. Our numerical results show that the momentum-related corrections are unfavorable to the formation of the molecular states in the $I=0$, $J^{PC}=1^{++}$ and $I=1$, $J^{PC}=1^{+-}$ channels in the $D{\bar{D}}^{\ast }$ systems.

Comments: 14 pages, 10 figures