Once these have been determined in a specific renormalization scheme then the anomalous dimension matrix is deduced from $$\gamma^{\cal O}_{ij} ~=~ \mu \frac{d ~}{d \mu}
\ln Z^{\cal O}_{ij}
\label{mixmatdef}$$ with $$\mu \frac{d~}{d\mu} ~=~ \beta(a) \frac{\partial ~}{\partial a} ~+~
\alpha \gamma_\alpha(a,\alpha) \frac{\partial ~}{\partial \alpha} 
\label{muderiv}$$ where $\alpha$ is the gauge parameter of the canonical linear covariant gauge and $\alpha$ $=$ $0$ corresponds to the Landau gauge. Although the operators we are considering are gauge invariant, in a mass dependent renormalization scheme, such as RI${}^\prime$ or RI${}^\prime$/SMOM, the anomalous dimensions can depend on the gauge. This is why we have included the second term on the right side of (\[muderiv\]). However, for the one loop computation here the leading term is scheme independent so that there is no gauge dependence at this order. In order to compare with the structure of our RI${}^\prime$/SMOM results later, we recall the three loop ${\overline{\mbox{MS}}}$ scheme anomalous dimension mixing matrices, [@36], are $$\begin{aligned}
\gamma^{W_2}_{11}(a) &=& \frac{8}{3} C_F a ~+~ \frac{1}{27} \left[ 376 C_A C_F
- 112 C_F^2 - 128 C_F T_F {N_{\!f}}\right] a^2 \nonumber \\
&& +~ \frac{1}{243} \left[ \left( 5184 \zeta(3) + 20920 \right) C_A^2 C_F
- \left( 15552 \zeta(3) + 8528 \right) C_A C_F^2 