The Combined Fit

Using the WVCXME reweighting scheme the final fitted values for the CP-conserving couplings are:

$\displaystyle \Delta\kappa_{\gamma}$	$\displaystyle =$	$\displaystyle -0.235^{+0.232}_{-0.200}$
$\displaystyle \Delta g^{Z}_{1}$	$\displaystyle =$	$\displaystyle -0.049^{+0.081}_{-0.080}$
$\displaystyle \lambda$	$\displaystyle =$	$\displaystyle -0.075^{+0.090}_{-0.081}$

Using the BILGOU reweighting scheme the final fitted values for the CP-conserving couplings are:

$\displaystyle \Delta\kappa_{\gamma}$	$\displaystyle =$	$\displaystyle -0.248^{+0.222}_{-0.197}$
$\displaystyle \Delta g^{Z}_{1}$	$\displaystyle =$	$\displaystyle -0.050^{+0.080}_{-0.078}$
$\displaystyle \lambda$	$\displaystyle =$	$\displaystyle -0.070^{+0.089}_{-0.078}$

Using the BILGOU reweighting scheme the final fitted values for the CP-violating couplings are:

$\displaystyle \tilde{\kappa}_{Z}$	$\displaystyle =$	$\displaystyle -0.191^{+0.062}_{-0.054}$
$\displaystyle \tilde{\lambda}_{Z}$	$\displaystyle =$	$\displaystyle -0.191^{+0.182}_{-0.126}$
$\displaystyle g^{Z}_{4}$	$\displaystyle =$	$\displaystyle +0.009^{+0.224}_{-0.223}$

The $\chi ^{2}$ plots for all these fits can be seen in figures 7.3, 7.4 and 7.5.

**Figure 7.3:** $\chi ^{2}$ plots of the fit of the CP-conserving couplings using the WVCXME reweighting scheme. The dashed line is the fit to single W SDM elements. the dotted line is the fit to the $\cos\theta_{\rm W}$ distribution, and the solid line is the combined fit.
$\begin{figure}\begin{center} \epsfig{file=figs/chiwvc.eps,width=1.1\linewidth}\end{center}\end{figure}$

**Figure 7.4:** $\chi ^{2}$ plots of the fit of the CP-conserving couplings using the BILGOU reweighting scheme. The dashed line is the fit to single W SDM elements, the dotted line is the fit to the $\cos\theta_{\rm W}$ distribution, and the solid line is the combined fit.
$\begin{figure}\begin{center} \epsfig{file=figs/chibil.eps,width=1.1\linewidth}\end{center}\end{figure}$

**Figure 7.5:** $\chi ^{2}$ plots of the fit of the CP-violating couplings using the BILGOU reweighting scheme. The dashed line is the fit to single W SDM elements, the dotted line is the fit to the $\cos\theta_{\rm W}$ distribution, and the solid line is the combined fit.
$\begin{figure}\begin{center} \epsfig{file=figs/chibilcp.eps,width=1.1\linewidth}\end{center}\end{figure}$

As mentioned earlier, the $\cos\theta_{\rm W}$ is much more sensitive to the CP-conserving couplings than the SDM elements are. This means that the fit to $\cos\theta_{\rm W}$ dominates the overall result. However, for the CP-violating couplings the converse is true, the $\cos\theta_{\rm W}$ distribution is much less sensitive to these couplings and therefore the fit to the SDM elements dominates the overall results.

The goodness of the fit is given by the absolute value of the $\chi ^{2}$ . The calculated values of the $\chi ^{2}$ for the combined fit for each coupling is given in table 7.2. For a good fit there should be a $\chi ^{2}$ of one per degree of freedom. The values calculated with the WVCXME give a lower $\chi ^{2}$ than BILGOU thus suggesting a slightly better fit.

Table 7.2: Absolute values of the $\chi ^{2}$ minimum for each measured coupling using the combined fit.

Coupling	WVCXME	BILGOU
$\Delta\kappa_{\gamma}$	53.6	57.8
$\Delta g^{z}_{1}$	54.2	58.6
$\lambda$	53.8	58.6
$\tilde{\kappa}_{z}$	-	74.7
$\tilde{\lambda}_{z}$	-	77.9
$g^{z}_{4}$	-	78.7