9.1 \(a_{\mu}^{SD}(\ell)\)

\(a^2(\mbox{fm})\)	\(a_{\mu}^{SD}(\ell)\)	r
0.0063387	45.582(21)	0
0.0063387	45.584(16)	0
0.0046522	46.288(14)	0
0.0032397	46.874(17)	0
0.0063387	40.347(37)	1
0.0063387	40.413(26)	1
0.0046522	42.252(31)	1
0.0032397	43.955(30)	1

9.1.1 linear

The continuum fit is done with the function \[ \begin{cases} a_{\mu}^{SD}(eq,\ell)=P[0]+a^2P[1]\\ a_{\mu}^{SD}(op,\ell)=P[0]+a^2P[2] \end{cases} \]

\[\begin{gather} \chi^2/d.o.f.=15.4204 \\ P[0]=4.80833e-09\pm (2.3e-12) \\ P[1]=-3.90223e-08\pm (4.3e-10) \\ P[2]=-1.22691e-07\pm (4.1e-10) \\ \end{gather}\] {\[\begin{gather} C=\begin{pmatrix} 1& -0.955& -0.888\\ -0.955& 1& 0.829\\ -0.888& 0.829& 1\\ \end{pmatrix} \\det=0\\ \end{gather}\]}

9.1.2 quadratic

The continuum fit is done with the function \[ \begin{cases} a_{\mu}^{SD}(eq,\ell)=P[0]+a^2P[1]+a^4P[3]\\ a_{\mu}^{SD}(op,\ell)=P[0]+a^2P[2]+a^4P[4] \end{cases} \]

\[\begin{gather} \chi^2/d.o.f.=0.762594 \\ P[0]=4.82364e-09\pm (1.4e-11) \\ P[1]=-4.21295e-08\pm (6.2e-09) \\ P[2]=-1.41317e-07\pm (6.4e-09) \\ P[3]=4.38735e-08\pm (6.3e-07) \\ P[4]=2.76401e-06\pm (6.6e-07) \\ \end{gather}\] {\[\begin{gather} C=\begin{pmatrix} 1& -0.995& -0.988& 0.987& 0.969\\ -0.995& 1& 0.992& -0.998& -0.977\\ -0.988& 0.992& 1& -0.989& -0.995\\ 0.987& -0.998& -0.989& 1& 0.977\\ 0.969& -0.977& -0.995& 0.977& 1\\ \end{pmatrix} \\det=0\\ \end{gather}\]}

9.1.3 quadratic eq

The continuum fit is done with the function \[ \begin{cases} a_{\mu}^{SD}(eq,\ell)=P[0]+a^2P[1]+a^4P[3]\\ a_{\mu}^{SD}(op,\ell)=P[0]+a^2P[2] \end{cases} \]

\[\begin{gather} \chi^2/d.o.f.=4.12553 \\ P[0]=4.76984e-09\pm (3.9e-12) \\ P[1]=-1.91082e-08\pm (1.5e-09) \\ P[2]=-1.15647e-07\pm (7.1e-10) \\ P[3]=-2.2696e-06\pm (1.5e-07) \\ \end{gather}\] {\[\begin{gather} C=\begin{pmatrix} 1& -0.939& -0.962& 0.819\\ -0.939& 1& 0.933& -0.962\\ -0.962& 0.933& 1& -0.842\\ 0.819& -0.962& -0.842& 1\\ \end{pmatrix} \\det=0\\ \end{gather}\]}

9.1.4 Simpson 3/8

\[\begin{gather} \chi^2/d.o.f.=0.742964 \\ P[0]=4.8462e-09\pm (1.4e-11) \\ P[1]=-5.79924e-08\pm (6.2e-09) \\ P[2]=-1.59258e-07\pm (6.4e-09) \\ P[3]=1.42438e-06\pm (6.3e-07) \\ P[4]=4.18583e-06\pm (6.6e-07) \\ \end{gather}\] {\[\begin{gather} C=\begin{pmatrix} 1& -0.996& -0.988& 0.987& 0.968\\ -0.996& 1& 0.992& -0.998& -0.977\\ -0.988& 0.992& 1& -0.989& -0.995\\ 0.987& -0.998& -0.989& 1& 0.977\\ 0.968& -0.977& -0.995& 0.977& 1\\ \end{pmatrix} \\det=0\\ \end{gather}\]}