Fit to the Normalised $\cos\theta_{\rm W}$ Distribution

Figure 7.2 shows the normalised $\cos\theta_{\rm W}$ distribution extracted from the 189 GeV data.

Figure: Normalised $\cos\theta_{\rm W}$ disribution extracted from the 189 GeV data (points). The solid line is the Standard Model prediction, the dotted is the predictions for $\Delta g^{z}_{1}$ $= +0.5$ and the dashed line is the prediction for $g^{z}_{4}$ $=+1.5$.

The fitted values using the WVCXME reweighting scheme are:

$$\Delta\kappa_{\gamma} = -0.267^{+0.297}_{-0.245}$$

$$\Delta g^{Z}_{1} = -0.075^{+0.085}_{-0.081}$$

$$\lambda = -0.090^{+0.091}_{-0.088}$$

And for the BILGOU reweighting scheme the fitted values are:

$$\Delta\kappa_{\gamma} = -0.265^{+0.285}_{-0.244}$$

$$\Delta g^{Z}_{1} = -0.070^{+0.089}_{-0.081}$$

$$\lambda = -0.090^{+0.093}_{-0.085}$$

The agreement between the two methods is once again very good, with agreement between each measured coupling using the two methods being better than 5% of the statistical error.

The $\chi ^{2}$ plots for the WVCXME and BILGOU fits are represented by the dotted lines shown in figures 7.3 and 7.4 respectively.

The fitted values for the CP-violating couplings are:

$$\tilde{\kappa}_{Z} = -0.189^{+0.444}_{-0.085}$$

$$\tilde{\lambda}_{Z} = -0.289^{+0.669}_{-0.122}$$

$$g^{Z}_{4} = +0.672^{+0.371}_{-1.710}$$

The $\chi ^{2}$ plots are the dotted lines shown in figure 7.5. All plots show a double minimum for the fit of CP-violating couplings. The sign of the coupling has no effect on the $\cos\theta_{\rm W}$ distribution, only the magnitude, so this double minimum is expected.