{\cal O}_2 & = & 
\frac{1}{2N} (\bar q_1 \gamma_\mu^L q_2)(\bar q_3 \gamma_\mu^R q_4)
+ (\bar q_1 T^A \gamma_\mu^L q_2)(\bar q_3 T^A \gamma_\mu^R q_4) ,\end{aligned}$$ where $\gamma_\mu^{L,R} = \gamma_\mu P_{L,R}$. Summation over repeated indices such as $\mu$ and $A$ is assumed. We note that $q_i$ $(i=1,2,3,4)$ are boundary quark fields in DWQCD. For the convenience of calculation we rewrite the above operators as $$\begin{aligned}
{\cal O}_\pm & = & \frac{1}{2}
\left[1{\widetilde{\otimes}}1 \pm 1{\widetilde{\odot}}1\right]^{ab;cd} 
\left[(\bar q_1^a \gamma_\mu^L q_2^b)
(\bar q_3^c \gamma_\mu^L q_4^d)\right], \\
{\cal O}_1 & = & \frac{1}{2} 
\left[-N 1{\widetilde{\otimes}}1 + 1{\widetilde{\odot}}1\right]^{ab;cd}  
\left[(\bar q_1^a \gamma_\mu^L q_2^b)
(\bar q_3^c \gamma_\mu^R q_4^d)\right], \\
{\cal O}_2 & = & \frac{1}{2}
\left[1{\widetilde{\odot}}1\right]^{ab;cd}  
\left[(\bar q_1^a \gamma_\mu^L q_2^b)
(\bar q_3^c \gamma_\mu^R q_4^d)\right], \end{aligned}$$ where $a,b,c,d$ are color indices, and ${\widetilde{\otimes}}$, ${\widetilde{\odot}}$ represent the tensor structures in the color space: $$\begin{aligned}
\left[1 {\widetilde{\otimes}} 1\right]^{ab;cd} & \equiv & \delta_{ab}\delta_{cd}, \\ 
\left[1 {\widetilde{\odot}} 1\right]^{ab;cd}  & \equiv & \delta_{ad}\delta_{cb}. \end{aligned}$$ To derive these formula, we have used the Fierz transformation for ${\cal O}_\pm$ and the formula $$\sum_A T^A{\widetilde{\otimes}} T^A = \frac{1}{2}\left[
-\frac{1}{N} 1{\widetilde{\otimes}} 1+1{\widetilde{\odot}} 1\right]$$ for ${\cal O}_{1,2}$ .

We calculate the following Green function: $$\langle {\cal O}_\Gamma \rangle_{\alpha\beta;\gamma\delta}^{ij;kl}
\equiv {\langle  {\cal O}_\Gamma (q_1)_{\alpha}^i (\bar q_2)_{\beta}^j
(q_3)_{\gamma}^k (\bar q_4)_{\delta}^l  \rangle},$$ where 