33.2 g10

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

\[\begin{gather} \chi^2/d.o.f.=0.182801 \\ P[0]=3.02175\pm (0.00019) \\ P[1]=-5.13265e-07\pm (1.7e-07) \\ P[2]=-80.0945\pm (19) \\ P[3]=3.55979\pm (0.83) \\ \end{gather}\] {\[\begin{gather} C=\begin{pmatrix} 1& -0.978& -0.155& 0.133\\ -0.978& 1& 0.253& -0.238\\ -0.155& 0.253& 1& -0.999\\ 0.133& -0.238& -0.999& 1\\ \end{pmatrix} \end{gather}\]}

33.2.0.1 with covariance matrix

\[\begin{gather} \chi^2/d.o.f.=1.16281e+07 \\ P[0]=3\pm (0) \\ P[1]=0.000102083\pm (0) \\ P[2]=254.085\pm (0) \\ P[3]=-10.0645\pm (6.4e-15) \\ \end{gather}\] {\[\begin{gather} C=\begin{pmatrix} -nan& -nan& -nan& -nan\\ -nan& -nan& -nan& -nan\\ -nan& -nan& -nan& -nan\\ -nan& -nan& -nan& 1\\ \end{pmatrix} \end{gather}\]}

33.2.1 g10 closer to the pole

fiting only the points close to the pole

\[\begin{gather} \chi^2/d.o.f.=0.0225297 \\ P[0]=3.02186\pm (0.00018) \\ P[1]=2.71872e-07\pm (2.8e-07) \\ P[2]=-74.2077\pm (19) \\ P[3]=3.35897\pm (0.84) \\ \end{gather}\] {\[\begin{gather} C=\begin{pmatrix} 1& -0.995& 0.0297& -0.0407\\ -0.995& 1& 0.0589& -0.0493\\ 0.0297& 0.0589& 1& -0.999\\ -0.0407& -0.0493& -0.999& 1\\ \end{pmatrix} \end{gather}\]}

33.2.2 g10 plus const

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

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

\[\begin{gather} \chi^2/d.o.f.=0.0001263 \\ P[0]=3.02179\pm (0.00022) \\ P[1]=-2.64813e-07\pm (5.5e-08) \\ P[2]=-94.2135\pm (18) \\ P[3]=4.11499\pm (0.8) \\ P[4]=1786.88\pm (7.9e+02) \\ P[5]=-68.4114\pm (37) \\ \end{gather}\] {\[\begin{gather} C=\begin{pmatrix} 1& -0.319& 0.126& -0.122& 0.0233& -0.00929\\ -0.319& 1& 0.35& -0.407& -0.919& 0.894\\ 0.126& 0.35& 1& -0.998& -0.167& 0.0938\\ -0.122& -0.407& -0.998& 1& 0.23& -0.158\\ 0.0233& -0.919& -0.167& 0.23& 1& -0.997\\ -0.00929& 0.894& 0.0938& -0.158& -0.997& 1\\ \end{pmatrix} \end{gather}\]}

33.2.3 g10 Breit-Wigner

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

\[\begin{gather} \chi^2/d.o.f.=2.27917 \\ P[0]=3.02178\pm (0.00034) \\ P[1]=5.82432e-05\pm (1.4e-05) \\ P[2]=-24.6876\pm (5.8) \\ P[3]=6019.8\pm (1.3e+03) \\ \end{gather}\] {\[\begin{gather} C=\begin{pmatrix} 1& -0.998& 0.334& 0.171\\ -0.998& 1& -0.316& -0.182\\ 0.334& -0.316& 1& -0.865\\ 0.171& -0.182& -0.865& 1\\ \end{pmatrix} \end{gather}\]}

33.2.4 g10 F fit

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

\[\begin{gather} \chi^2/d.o.f.=1.52965 \\ P[0]=-4.47071e-06\pm (3.6e-08) \\ P[1]=1.62498e-06\pm (2.5e-13) \\ P[2]=3.69096e-06\pm (3.9e-09) \\ P[3]=-1.79208e-07\pm (1.8e-12) \\ \end{gather}\] {\[\begin{gather} C=\begin{pmatrix} 1& 0.972& 1& 1\\ 0.972& 1& 0.972& 0.971\\ 1& 0.972& 1& 1\\ 1& 0.971& 1& 1\\ \end{pmatrix} \end{gather}\]}

pole position \(1/K +F=0\) in \(E/M_0\) \[ pole=3.02179 (0.000223615) -i 1.64916e-07 (3.16526e-08) \]