Tests of CP-Invariance

Measurement of the CP-violating TGCs was performed by combing information from the SDM elements and from the W production angle. Constraining the interaction to ${\rm SU}(2)_{L}\times {\rm U}(1)_{Y}$ gauge invariance, the values obtained are as follows:

$\displaystyle \tilde{\kappa}_{Z}$	$\displaystyle =$	$\displaystyle -0.184^{+0.091}_{-0.065}$
$\displaystyle \tilde{\lambda}_{Z}$	$\displaystyle =$	$\displaystyle -0.136^{+0.161}_{-0.194}$
$\displaystyle g^{Z}_{4}$	$\displaystyle =$	$\displaystyle +0.070^{+0.263}_{-0.255}$

The errors on these results are due to both statistical and systematic uncertainties.

Within the Standard Model at tree level there is no CP-violation at the WW ${\rm Z}^{0}$ and WW $\gamma$ vertex, therefore the CP-violating TGCs are zero. The measured values of the couplings are all consistent with the Standard Model expectations.

A further test of CP-invariance in the W-pair production process is given by the imaginary parts of the single W SDM elements. At tree level CP-invariance requires the following:

$\displaystyle Im\left(\rho^{W^{-}}_{\tau\tau^{\prime}}(s,\cos\theta_{W})\right) - Im\left(\rho^{W^{+}}_{-\tau^{\prime}-\tau}(s,\cos\theta_{W})\right) = 0$

(11.1)

This equation gives a completely Model independent test of CP-violation in the W-pair production process. Plots of the combinations of imaginary SDM observables needed to test CP-invariance calculated from the 189 GeV data can be seen in figure 11.1. No obvious deviations from zero are observed. Calculating the $\chi ^{2}$ for each plot, the following are obtained:

$\displaystyle \chi^{2}:Im\left(\rho^{W^{-}}_{+-}(s,k)\right) - Im\left(\rho^{W^{+}}_{-+}(s,k)\right)$	$\displaystyle =$	$\displaystyle 6.48$
$\displaystyle \chi^{2}:Im\left(\rho^{W^{-}}_{+0}(s,k)\right) - Im\left(\rho^{W^{+}}_{-0}(s,k)\right)$	$\displaystyle =$	$\displaystyle 8.90$
$\displaystyle \chi^{2}:Im\left(\rho^{W^{-}}_{-0}(s,k)\right) - Im\left(\rho^{W^{+}}_{+0}(s,k)\right)$	$\displaystyle =$	$\displaystyle 6.77$

The $\chi ^{2}$ includes both statistical and systematic uncertaintes. As each histogram contains eight degrees of freedom, these results are consistent with Standard Model expectations.

**Figure 11.1:** The three plots on the left give a test of CP-violation at tree level. Any deviation from zero could only be caused by CP-violation. Overlaid on these plots are the analytical predictions for CP-violating couplings $\tilde{\lambda}_{z}$ = 0.5 (dotted line) and $\tilde{\kappa}_{z}$ = 0.5 (dashed line). The three plots on the right give a test of CPT-invariance and effects beyond tree level. Any deviation from zero could only be caused by effects beyond tree level or CPT-violation.
$\begin{figure}\begin{center} \epsfig{file=figs/final2.eps,width=1\linewidth}\end{center}\end{figure}$

Also included in figure 11.1 are the plots that test for effects beyond tree level, as discussed in chapter 3, equation 3.48. Any deviations in these plots could only be due to effects beyond tree level or CPT-violation. No obvious deviations from zero are seen. Calculating the $\chi ^{2}$ for each plot, the following results are obtained:

$\displaystyle \chi^{2}:Im\left(\rho^{W^{-}}_{+-}(s,k)\right) + Im\left(\rho^{W^{+}}_{-+}(s,k)\right)$	$\displaystyle =$	$\displaystyle 4.12$
$\displaystyle \chi^{2}:Im\left(\rho^{W^{-}}_{+0}(s,k)\right) + Im\left(\rho^{W^{+}}_{-0}(s,k)\right)$	$\displaystyle =$	$\displaystyle 5.63$
$\displaystyle \chi^{2}:Im\left(\rho^{W^{-}}_{-0}(s,k)\right) + Im\left(\rho^{W^{+}}_{+0}(s,k)\right)$	$\displaystyle =$	$\displaystyle 7.56$