Possible $D_{1}D_{1}$, $D_{1} \bar D_{1} $, $B_{1}B_{1}$ and $B_{1} \bar B_{1} $ molecular states and the recoil corrections

Abstract

Recoil correction appears at $O(\frac{1}{M})$, which turns out to be very essential for the hadronic molecules with heavy flavor. In the past, we always thought that the recoil corrections were unfavorable to the formation of the molecular states, but our research reveals its importance to form the di-hadron bound states. In some cases, we are unable to find the bound states without considering the recoil corrections. Under SU(2) chiral symmetry, we have studied the $D_1 D_1$, $D_1 \bar D_1$, $B_1 B_1$ and $B_1 \bar B_1$ systems in the framework of the one-boson exchange (OBE) model with the treatments of the $S$\--{}$D$ wave mixing effect and the recoil corrections. Our results indicate that both the $D_1 D_1$ system with $I(J^P)=0(1^+)$ and $I(J^P)=1(2^+)$ can form the molecular states whether with the recoil corrections or not, while the $D_1 D_1$ system with $I(J^P)=1(0^+)$ fail to form a hadronic molecule without the recoil corrections but it turns out to be a loosely bound state after the inclusion of the recoil corrections. And we have found the deuteron-like states for the $D_1 \bar D_1$, $B_1 B_1$ and $B_1 \bar B_1$ systems, whether considering the recoil corrections or not.