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

TL;DR

This paper investigates the effects of recoil corrections and spin-orbit forces on the potential formation of molecular states composed of heavy mesons $B^* ar{B}^{*}$ and $D^* ar{D}^{*}$ using a one-boson exchange model.

Contribution

It introduces recoil corrections up to order 1/M^2 in the potential calculations, highlighting their importance for loosely bound heavy meson molecular states.

Findings

Recoil corrections favor the formation of certain molecular states.

Momentum-related corrections are significant for binding.

Results support possible molecular states with specific quantum numbers.

Abstract

In the framework of the one-boson exchange model, we have calculated the effective potentials between two heavy mesons $B^* \bar{B}^{*}$ and $D^* \bar{D}^{*}$ from the t- and u-channel $\pi$-, $\eta$-, $\rho$-, $\omega$- and $\sigma$-meson exchanges. We keep the recoil corrections to the $B^* \bar{B}^{*}$ and $D^* \bar{D}^{*}$ 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 $B^* \bar{B}^{*}$ and $D^* \bar{D}^{*}$ systems.