D^\beta \psi_f $ is the quark component to the traceless part of the energy-momentum tensor, $D^\mu\equiv \partial^\mu +igA^\mu_a t^a$ is the covariant derivative, $A^\mu_a$ is the gluon field, $t^a$ is the generator of the $SU({N_c})$ group in the fundamental representation, $f_{abc}$ is the structure constant of the $SU({N_c})$ group, $m_f$ is the current quark mass, $g$ is the QCD coupling constant, $\alpha_s\equiv g^2/(4\pi)$, and ${N_c}$ is the number of the colors. ${\cal {ST}}$ makes a tensor symmetric and traceless, ${\cal {ST}}O^{\alpha\beta}\equiv (O^{\alpha\beta}+O^{\beta\alpha})/2-g^{\alpha\beta}O^\mu_\mu /4$.

We decompose Eq.(\[eq:OPE\]) into transverse and longitudinal components as $$\begin{aligned}
\nonumber
\delta G_{T}(\omega,{{\mathbf{p}}}) 
&=e^2\sum q^2_f \frac{1}{p^2} \\
\nonumber
&~~~\times \Bigl[\left\{2m_f \delta\left\langle\overline{\psi}_f \psi_f \right\rangle
+\frac{1}{12}\delta\left\langle \frac{\alpha_s}{\pi}G^2\right\rangle \right\}\\
\label{eq:OPE-wo-RG-T}
&~~~+\frac{8}{3}\frac{\omega^2+{{\mathbf{p}}}^2}{p^2}\delta\left\langle T^{00}_f \right\rangle 
\Bigr]
+{\cal O}(\omega^{-4}),\\
\nonumber
\delta G^{R}_{00}(\omega,{{\mathbf{p}}}) 
&=e^2\sum q^2_f \frac{1}{p^2}\frac{{{\mathbf{p}}}^2}{p^2} \\ 
\nonumber
&~~~\times \Bigl[\left\{2m_f \delta\left\langle\overline{\psi}_f \psi_f \right\rangle
+\frac{1}{12}\delta\left\langle \frac{\alpha_s}{\pi}G^2\right\rangle \right\} \\
\label{eq:OPE-wo-RG-L}
&~~~+\frac{8}{3} \delta\left\langle T^{00}_f \right\rangle  
\Bigr]
+{\cal O}(\omega^{-6}),\end{aligned}$$ where we have used the isotropy of the system and the traceless property of $T^{\alpha\beta}_f$.

Because we consider the $\omega\rightarrow \infty$ limit, we need to take into account the rescaling/mixing effect of the operators. Due to their vanishing anomalous dimensions, the chiral and gluon condensate terms remain unchanged, but the quark component of the energy-momentum tensor changes. To describe 