7.5 QC3 fit g0

7.5.1 no resonace antsaz g0 kcot1par

\[ F_{3}^{iso}(E,\vec{P},L)=-1/{ K}_{df}^{iso}(E^*) \]

\[ K_{df}^{iso}= P[0] \]

\[ F_{3}^{iso}(E,\vec{P}=0,L)=\frac{1}{L}\left[ \frac{\tilde F^s}{3}- \tilde F^s\frac{1}{1/(2\omega K_2^s)+\tilde F^s+\tilde G^s}\tilde F^s\right]_{kp}\\ \left[\frac{1}{2\omega K_2^s}\right]_{kp}=\delta_{kp}\left[(k\cot\delta )+|q^*_{2,k}(1-H(\vec{k}))|\right]\frac{1}{32\pi\omega_k E_{2,k}^*} \] and \[ \frac{k}{m} \cot \delta= \frac{1}{a_0m}\\ P[2]=am\\ P[3]=r_0m \] \[ E_{\phi_1}= p[1] \]

The best fit:

\[\begin{gather} \chi^2/d.o.f.=1.83686 \\ P[0]=1351.93\pm (4.9e+02) \\ P[1]=3.03431\pm (0.00032) \\ P[2]=-0.15141\pm (0.0018) \\ \end{gather}\] {\[\begin{gather} C=\begin{pmatrix} 1& 193& -399\\ 193& 1& -0.000163\\ -399& -0.000163& 1\\ \end{pmatrix} \end{gather}\]}

7.5.2 resonace antsaz g0

Here we want to check if at \(g=0\) are able to exclude the parametrization with a pole

\[ F_{3}^{iso}(E,\vec{P},L)=-1/{ K}_{df}^{iso}(E^*) \]

\[ K_{df}^{iso}= \frac{P[0]M_0^2}{E^2-M_R^2}+P[2] \]

\[ F_{3}^{iso}(E,\vec{P}=0,L)=\frac{1}{L}\left[ \frac{\tilde F^s}{3}- \tilde F^s\frac{1}{1/(2\omega K_2^s)+\tilde F^s+\tilde G^s}\tilde F^s\right]_{kp}\\ \left[\frac{1}{2\omega K_2^s}\right]_{kp}=\delta_{kp}\left[(k\cot\delta )+|q^*_{2,k}(1-H(\vec{k}))|\right]\frac{1}{32\pi\omega_k E_{2,k}^*} \] and \[ \frac{k}{m} \cot \delta= \frac{1}{a_0m}\\ P[2]=am\\ P[3]=r_0m \] \[ E_{\phi_1}= p[1] \]

The best fit:

\[\begin{gather} \chi^2/d.o.f.=1.67469 \\ P[0]=10.4888\pm (6.2) \\ P[1]=9.20721\pm (0.0019) \\ P[2]=1474.94\pm (4.4e+02) \\ P[3]=-0.151661\pm (0.0017) \\ \end{gather}\] {\[\begin{gather} C=\begin{pmatrix} 1& 0.081& 1.73& -1.4\\ 0.081& 1& 0.000681& -0.00113\\ 1.73& 0.000681& 1& -372\\ -1.4& -0.00113& -372& 1\\ \end{pmatrix} \end{gather}\]}