### 9.3.1 amu_sd_l_reinman_log_eq_a4_eq_Mpi_op_cov

$\begin{cases} a_{\mu}^{SD}(eq,\ell)=P[0]+ \frac{a^2}{(\log a^2/w_0^2)^3}P[1] +a^4P[3] \\ a_{\mu}^{SD}(op,\ell)=P[0]+a^2P[2]+ P[4](M_{\pi}^2-M_{\pi,phys}^2) \end{cases}$

$\begin{gather} \chi^2/d.o.f.=1.5501 \\ P[0]=4.75594e-09\pm (3.2e-12) \\ P[1]=-1.17439e-07\pm (1e-08) \\ P[2]=-1.15489e-07\pm (8e-10) \\ P[3]=-9.77275e-06\pm (4.9e-07) \\ P[4]=7.89896e-09\pm (1.7e-09) \\ \end{gather}$ {$\begin{gather} C=\begin{pmatrix} 1& -0.877& -0.643& -0.918& -0.174\\ -0.877& 1& 0.53& 0.994& 0.233\\ -0.643& 0.53& 1& 0.559& -0.588\\ -0.918& 0.994& 0.559& 1& 0.225\\ -0.174& 0.233& -0.588& 0.225& 1\\ \end{pmatrix} \\det=0\\ \end{gather}$}

### 9.3.2 amu_sd_l_reinman__a4_eq_Mpi_eq_op_cov

$\begin{cases} a_{\mu}^{SD}(eq,\ell)=P[0]+ a^2P[1] +a^4P[3] +P[4](M_{\pi}^2-M_{\pi,phys}^2)\\ a_{\mu}^{SD}(op,\ell)=P[0]+a^2P[2]+ P[4](M_{\pi}^2-M_{\pi,phys}^2) \end{cases}$

$\begin{gather} \chi^2/d.o.f.=1.5501 \\ P[0]=4.75594e-09\pm (3.2e-12) \\ P[1]=-1.17439e-07\pm (1e-08) \\ P[2]=-1.15489e-07\pm (8e-10) \\ P[3]=-9.77275e-06\pm (4.9e-07) \\ P[4]=7.89896e-09\pm (1.7e-09) \\ \end{gather}$ {$\begin{gather} C=\begin{pmatrix} 1& -0.877& -0.643& -0.918& -0.174\\ -0.877& 1& 0.53& 0.994& 0.233\\ -0.643& 0.53& 1& 0.559& -0.588\\ -0.918& 0.994& 0.559& 1& 0.225\\ -0.174& 0.233& -0.588& 0.225& 1\\ \end{pmatrix} \\det=0\\ \end{gather}$}

### 9.3.3 amu_sd_l_reinman_log_eq_a4_op_Mpi_eq_cov

$\begin{cases} a_{\mu}^{SD}(eq,\ell)=P[0]+ \frac{a^2}{(\log a^2/w_0^2)^3}P[1] +P[4](M_{\pi}^2-M_{\pi,phys}^2)\\ a_{\mu}^{SD}(op,\ell)=P[0]+a^2P[2]+a^4P[3] \end{cases}$

$\begin{gather} \chi^2/d.o.f.=6.883 \\ P[0]=4.69384e-09\pm (1.7e-12) \\ P[1]=9.54216e-08\pm (1.2e-09) \\ P[2]=-8.45956e-08\pm (1.2e-09) \\ P[3]=-2.98914e-06\pm (1.9e-07) \\ P[4]=1.08081e-08\pm (1.3e-09) \\ \end{gather}$ {$\begin{gather} C=\begin{pmatrix} 1& -0.00518& -0.56& 0.404& -0.725\\ -0.00518& 1& 0.305& -0.336& 0.506\\ -0.56& 0.305& 1& -0.972& 0.604\\ 0.404& -0.336& -0.972& 1& -0.52\\ -0.725& 0.506& 0.604& -0.52& 1\\ \end{pmatrix} \\det=0\\ \end{gather}$}