Mass of Y(3940) in Bethe-Salpeter equation for quarks

The general form of the Bethe-Salpeter wave functions for the bound states composed of two vector fields of arbitrary spin and definite parity is corrected. Using the revised general formalism, we investigate the observed \emph{Y}(3940) state which is considered as a molecule state consisting of $D^{\ast 0}{\bar{D}}^{\ast 0}$. Though the attractive potential between $D^{\ast 0}$ and ${\bar{D}}^{\ast 0}$ including one light meson ($\sigma$, $\pi$, $\omega$, $\rho$) exchange is considered, we find that in our approach the contribution from one-$\pi$ exchange is equal to zero and consider SU(3) symmetry breaking. The obtained mass of \emph{Y}(3940) is consistent with the experimental value.