\chi | - \delta_{ij}\,\Big[
\, \hat g_1\,\delta_{ab}\,\quarknumberoperator+\hat g_2\,
d_{abc}\,T^c  + \hat g_3\,\{T^a,\,T^b\}  + \hat g_4\,d_{abc}\, \{J_k,\,G_k^c\} 
\nonumber\\
& & \quad + \,\hat g_5\,\Big( \{ J_k,\, \{T^{a},\,G^{b}_k\} \} + \{ J_k,\,\{G^{a}_k,\,T^{b} \} \Big)   \Big]
+ \hat g_6\,\Big( \{G^{a}_i,\,G^{b}_j\}  +\{G^{a}_j,\,G^{b}_i \} \Big)
\nonumber\\
& &  + \,(\bar p+p)_i \,(\bar p+p)_j \,\Big[
 \,\hat g_7\,\delta_{ab}\,\quarknumberoperator+ \hat g_8\,
d_{abc}\,T^c + \hat g_9\,\{T^a,\,T^b \} + \hat g_{10}\,d_{abc}\, \{J_k,\,G_k^c\} 
\nonumber\\
& & \quad 
+ \,\hat g_{11}\,\Big( \{ J_k,\, \{T^{a},\,G^{b}_k\} \} + \{ J_k,\,\{G^{a}_k,\,T^{b} \} \Big) \Big]
 \, | \chi ) + \cdots \,.
\label{QCD-identity-AA}\end{aligned}$$ A matching with the terms form (\[def-Q2-terms\]) leads to the following six sum rules $$\begin{aligned}
&& \bar g^{(S)}_F =  \bar g^{(S)}_0 + \frac{3}{2}\, \bar g^{(S)}_1 +  \bar g^{(S)}_D -  \bar h^{(S)}_1 - \frac{1}{3}\, \bar h^{(S)}_5 + \frac{2}{9}\, \bar h^{(S)}_6\,,
\nonumber\\
&&  \bar h^{(S)}_2 = 0\,, \qquad  \bar h^{(S)}_4 = -  \bar h^{(S)}_6\,,
\nonumber\\
&&  \bar h^{(S)}_3 = \frac{3}{2}\,\bar g^{(S)}_0 + \frac{15}{4}\, \bar g^{(S)}_1 + 3\, \bar g^{(S)}_D - \frac{3}{2}\, \bar h^{(S)}_1 
- \frac{3}{2}\, \bar h^{(S)}_5 + \frac{1}{3}\, \bar h^{(S)}_6\,, \qquad 
\nonumber\\ \nonumber\\      
&& \bar g^{(V)}_F =  \bar g^{(V)}_0 + \frac{3}{2}\, \bar g^{(V)}_1 +  \bar g^{(V)}_D -  \bar h^{(V)}_1 - \frac{1}{3}\, \bar h^{(V)}_3\,, \qquad
\nonumber\\      
&&   \bar h^{(V)}_2 = \frac{3}{2}\, \bar g^{(V)}_0 + \frac{15}{4}\, 