to the singlet state $(1)_T$, we have 10 neutral states from $(44)^{ij}$, in which { $(44)^{11}+(44)^{22}$, $(44)^{33}+(44)^{44}$, $(44)^{55}+(44)^{66}$, $(44)^{77}$, $(44)^{88}$ } are the diagonal element states ($i=j$), and {$(44)^{35}+(44)^{46}$, $(44)^{36}-(44)^{45}$, $(44)^{78}$, $(44)^{79}$, $(44)^{89}$} are the off-diagonal element states ($i\neq j$). Among the diagonal element states, the linear combination $(44)^{77}-(44)^{88}$ has different property under the transformation of $\chi_r \to \chi_i$ and $\chi_i \to - \chi_r$. Then, linear combinations { $(44)^{11}+(44)^{22}+(44)^{77}+(44)^{88}$, $(44)^{33}+(44)^{44}+(44)^{55}+(44)^{66}$ } and { $(44)^{11}+(44)^{22}-(44)^{77}-(44)^{88}$, $(44)^{33}+(44)^{44}-(44)^{55}-(44)^{66}$} show different property under the transformation of $\chi^{++}\chi^{--} \leftrightarrow \chi^0\chi^0$, and $\chi^{+}\chi^{-} \leftrightarrow \xi^+\xi^-$. The first two states have completely the same property as that of the singlet state $(1)_T$, so that the appropriate linear combination of these three states give the three eigenstates. For the off-diagonal element states, we can separate them by using the $C$ parity and the transformation of $\xi \to -\xi$, so that these states are block-diagonalized to two $2 \times 2$ submatrices and one singlet. By diagonalizing remained $2 \times 2$ matrices, we obtain all the eigenstates for the $\Psi_T\Psi_T \to \Psi_T\Psi_T$ channels.

In order to diagonalize all the $\Psi_D\Psi_D$ and $\Psi_T\Psi_T$ states, we take linear combinations of the eigenstates of $\Psi_D\Psi_D$ and $\Psi_T\Psi_T$ that have similar transformation properties. Consequently, 