B\right) \mathrm{tr} \left(\chi_+^2\right) + c_1\, \mathrm{tr} \left(\bar B \,\chi_+\right) \mathrm{tr}\left(\chi_+ B\right) \nonumber \\
&+& c_2\, \mathrm{tr} \left( \bar B\, \{\chi_+^2,\, B\} \right)  + c_3\,\mathrm{tr} \left( \bar B\, [\chi_+^2, \,B] \right)
\nonumber \\
&+& c_4\, \mathrm{tr} \left(\bar B\, \{\chi_+,\,B\} \right) \mathrm{tr} (\chi_+) + c_5\, \mathrm{tr}\left(\bar B\, [\chi_+,\,B]\right) \mathrm{tr} (\chi_+) \nonumber \\
&+& c_6\, \mathrm{tr} \left(\bar B \,B\right) \left(\mathrm{tr}(\chi_+)\right)^2
\nonumber \\
&-& e_0\, \mathrm{tr}\left(\bar B_\mu \cdot B^\mu \right) \mathrm{tr}\left(\chi_+^2\right) - e_1\, \mathrm{tr}\left( \left(\bar{B}_\mu \cdot \chi_+\right) \left(\chi_+ \cdot B^\mu\right) \right)
\nonumber \\
&-& e_2\, \mathrm{tr}\left( \left(\bar B_\mu \cdot B^\mu\right)\cdot \chi_+^2\right) - e_3\, \mathrm{tr}\left( \left(\bar B_\mu \cdot B^\mu\right)\cdot \chi_+\right) \mathrm{tr}(\chi_+) \nonumber \\
&-& e_4\, \mathrm{tr}\left(\bar B_\mu \cdot B^\mu\right) \left(\mathrm{tr}(\chi_+)\right)^2\,.
\label{def-c-e}\end{aligned}$$ Sum rules are derived by a study of the following matrix elements $$\begin{aligned}
&&i\, \int  d^4 x \,e^{-i\,q\cdot x}  \,{\langle \bar p\,,\,\bar\chi\,|}\, {\mathcal T}\,S^{(a)} (x)\,S^{(b)}(0) {|\,p\,,\chi \rangle}
=  {(\bar\chi\,|}\,\hat c_1\,\delta_{a0}\,\delta_{b0}\,{\mathbbm 1}
\nonumber\\
&& \quad \!+ \,\hat c_2\,\delta_{ab}\,{\mathbbm 1}
+ \hat c_3\,\big( T^a\,\delta_{b0} + \delta_{a0}\,T^b \big) 
+ \hat c_4\,d_{abc}\,T^c +\hat c_5\,\{ T^a,T^b\}
\nonumber\\
&&  \quad \!+\,  \hat c_6\,d_{abc}\,\{ J_i,G_i^c\}
 + \hat c_7\,\Big( \big\{ J_i\,,\,G_i^a \big\}\,\delta_{b0}
+ \delta_{a0}\,\big\{ J_i\,,\,G_i^b \big\}\Big)
\nonumber\\
&&  \quad \!+\, \hat c_8 \,\Big( \big\{ J_i\,,\big\{T^a,\,\,G_i^b \big\}\big\} +\big\{ J_i\,,\big\{T^b,\,\,G_i^a \big\}\big\} \Big)
{|\chi )} 
+ \cdots\,,
\label{SS-expanded}\end{aligned}$$ where we consider leading and subleading order 