33.3 g20

fit of \[ {\cal M}_{3s}(E)=\frac{\Gamma}{E^2-M_r^2} \] with

\[ M_r= P[0]+iP[1]\\ \Gamma= P[2]+iP[3] \]

here we took \(k_{df}\) from the \(g=20\) fit

\[\begin{gather} \chi^2/d.o.f.=1.42792e-05 \\ P[0]=-3.02112\pm (0.00026) \\ P[1]=3.89798e-07\pm (1.4e-07) \\ P[2]=-259.704\pm (21) \\ P[3]=10.5875\pm (1.2) \\ \end{gather}\] {\[\begin{gather} C=\begin{pmatrix} 1& -0.216& 0.377& -0.69\\ -0.216& 1& -0.596& 0.549\\ 0.377& -0.596& 1& -0.928\\ -0.69& 0.549& -0.928& 1\\ \end{pmatrix} \end{gather}\]}

33.3.1 g20 closer to the pole

fiting only the points close to the pole

\[\begin{gather} \chi^2/d.o.f.=6.13248e-07 \\ P[0]=-3.02112\pm (0.00026) \\ P[1]=4.18766e-07\pm (1.2e-07) \\ P[2]=-259.674\pm (21) \\ P[3]=10.6503\pm (1.1) \\ \end{gather}\] {\[\begin{gather} C=\begin{pmatrix} 1& -0.41& 0.379& -0.646\\ -0.41& 1& -0.667& 0.684\\ 0.379& -0.667& 1& -0.949\\ -0.646& 0.684& -0.949& 1\\ \end{pmatrix} \end{gather}\]}

33.3.2 g20 plus const

fit of \[ {\cal M}_{3s}(E)=\frac{\Gamma}{E^2-M_r^2}+a_0 \] with

\[ M_r= P[0]+iP[1]\\ \Gamma= P[2]+iP[3]\\ c=P[4]+iP[5] \]

\[\begin{gather} \chi^2/d.o.f.=8.48825e-07 \\ P[0]=3.02112\pm (0.00026) \\ P[1]=-4.30934e-07\pm (6.9e-08) \\ P[2]=-259.683\pm (26) \\ P[3]=10.6077\pm (1) \\ P[4]=-2981.99\pm (9.3e+02) \\ P[5]=-216.131\pm (3.6e+02) \\ \end{gather}\] {\[\begin{gather} C=\begin{pmatrix} 1& -0.591& -0.656& 0.25& 0.604& 0.991\\ -0.591& 1& 0.839& -0.759& -0.685& -0.518\\ -0.656& 0.839& 1& -0.861& -0.618& -0.58\\ 0.25& -0.759& -0.861& 1& 0.487& 0.157\\ 0.604& -0.685& -0.618& 0.487& 1& 0.506\\ 0.991& -0.518& -0.58& 0.157& 0.506& 1\\ \end{pmatrix} \end{gather}\]}

33.3.3 g20 Breit-Wigner

fit of \[ {\cal M}_{3s}(E)=\frac{R}{E-M_r+i\Gamma/2}+c \]

\[\begin{gather} \chi^2/d.o.f.=0.0415362 \\ P[0]=3.02109\pm (0.00081) \\ P[1]=-2.12263e-06\pm (0.00016) \\ P[2]=-47.9544\pm (9.6e+02) \\ P[3]=-266206\pm (7.3e+06) \\ \end{gather}\] {\[\begin{gather} C=\begin{pmatrix} 1& -0.458& -0.946& 0.88\\ -0.458& 1& 0.332& -0.373\\ -0.946& 0.332& 1& -0.971\\ 0.88& -0.373& -0.971& 1\\ \end{pmatrix} \end{gather}\]}

33.3.4 g20 F fit

fit of \[ F^{\infty}(E)=P[0]+P[1] \frac{E^2}{M_0^2} +i\left(P[2]+P[3] \frac{E^2}{M_0^2}\right) \]

\[\begin{gather} \chi^2/d.o.f.=0.314772 \\ P[0]=-4.41294e-06\pm (1.9e-08) \\ P[1]=1.43993e-06\pm (4.2e-12) \\ P[2]=3.6535e-06\pm (2.1e-09) \\ P[3]=-1.58932e-07\pm (4.7e-13) \\ \end{gather}\] {\[\begin{gather} C=\begin{pmatrix} 1& 1& 1& 1\\ 1& 1& 1& 1\\ 1& 1& 1& 1\\ 1& 1& 1& 1\\ \end{pmatrix} \end{gather}\]}

pole position \(1/K +F=0\) in E/M_0 \[ pole=3.02112 (0.000257856) -i 4.29618e-07 (4.97291e-08) \]