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 Y (3940) state, which is considered as a molecule state consisting of D ∗ 0 D ¯ ∗ 0 . Though the attractive potential between D ∗ 0 and D ¯ ∗ 0 including one light meson ( σ , π , ω , ρ ) exchange is considered, we find that in our approach the contribution from one- π exchange is equal to zero and consider SU(3) symmetry breaking. The obtained mass of Y (3940) is consistent with the experimental value.