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 \(D^{*0}\bar{D}^{*0}\). Though the attractive potential between \(D^{*0}\) and \(\bar{D}^{*0}\) 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.