Performance of Selection

The performance of the selection on CC03 Monte Carlo signal events is shown in table 5.6. The overall selection efficiency of the signal events is estimated to be (87.7 $\pm$ 1.1)%.

Figure 5.7 shows the $\cos\theta_{\rm W}$ distributions of all Monte Carlo events compared to that of selected events only from a sample of CC03 Monte Carlo.

Table: Variables used to calculate the relative likelihood of the ${\rm W}^{+}{\rm W}^{-}\rightarrow{\rm q}\bar{\rm q}\tau\bar{\nu}_{\tau}$ events. There is a different subset for each type of $\tau$ decay.

Variable	$\tau\rightarrow{\rm e}$	$\tau\rightarrow\mu$	$\tau\rightarrow1{\rm h}$	$\tau\rightarrow3{\rm h}$
$E_{\rm lepton}$	$\surd$	$\surd$	$\surd$	$\surd$
PR($\ell$)	$\surd$	$\surd$		$\surd$
$I_{200}$	$\surd$	$\surd$		$\surd$
$I_{200}^{\rm CT}$			$\surd$
$I_{200-500}$	$\surd$	$\surd$	$\surd$
$Y_{23}$			$\surd$	$\surd$
$\cos\theta_{\rm mis}$	$\surd$	$\surd$	$\surd$	$\surd$
$R_{\rm vis}$	$\surd$	$\surd$	$\surd$	$\surd$
$R_{\rm mis}$			$\surd$	$\surd$
$\sum P{\rm T}$	$\surd$	$\surd$	$\surd$	$\surd$
$\cos\theta_{\rm lpmis}$			$\surd$	$\surd$
P( $\sqrt{s^{\prime}}$)			$\surd$	$\surd$
$\sqrt{s^{\prime}}$	$\surd$	$\surd$	$\surd$	$\surd$
N $^{\rm min}_{\rm CT}$	$\surd$	$\surd$	$\surd$	$\surd$
N $^{\rm lepton-jet}_{\rm CT}$			$\surd$
E$_{\rm qq}$			$\surd$
$\cos\theta_{\ell,(\rm jet)}$	$\surd$	$\surd$	$\surd$	$\surd$

Figure: The $\cos\theta_{\rm W}$ distributions calculated for a sample of CC03 Monte Carlo. The yellow histogram represents all events and the green histogram is for selected events only.

The number of background events expected to be selected by this method calculated from Monte Carlo are shown in table 5.10. The expected selected cross-section is shown, along with the number of events this corresponds to in the 189 GeV data. Table 5.7 shows a summary of all these results, along with the actual number of events selected from the OPAL data. Good agreement is seen between the expected number of events and the selected number of events. The 1246 events actually selected consists of 389 ${\rm q}\bar{\rm q}{\rm e}\bar{\nu}_{\rm e}$, 420 ${\rm q}\bar{\rm q}\mu\bar{\nu}_{\mu}$ and 437 ${\rm q}\bar{\rm q}\tau\bar{\nu}_{\tau}$.

Table: The performance of the selection of events. Shown is the efficiency of selection each type of event. The first column indicates what the event was selected as and then the following columns indicate what percentage of each type of generated events was selected as the type indicated.

selected as	${\rm W}^{+}{\rm W}^{-}\rightarrow{\rm q}\bar{\rm q}{\rm e}\bar{\nu}_{\rm e}$	${\rm W}^{+}{\rm W}^{-}\rightarrow{\rm q}\bar{\rm q}\mu\bar{\nu}_{\mu}$	${\rm W}^{+}{\rm W}^{-}\rightarrow{\rm q}\bar{\rm q}\tau\bar{\nu}_{\tau}$
${\rm q}\bar{\rm q}{\rm e}\bar{\nu}_{\rm e}$	85.42 $\pm$ 0.84 %	0.12 $\pm$ 0.01 %	3.80 $\pm$ 0.50 %
${\rm q}\bar{\rm q}\mu\bar{\nu}_{\mu}$	0.15 $\pm$ 0.01 %	89.16 $\pm$ 0.80 %	4.30 $\pm$ 0.50 %
${\rm q}\bar{\rm q}\tau\bar{\nu}_{\tau}$	4.55 $\pm$ 0.50 %	4.41 $\pm$ 0.50 %	68.44 $\pm$ 1.44 %

Table 5.7: The expected number of events selected from each of the different processes. Also shown is the total number of observed events at 189 GeV.

Selected as	${\rm W}^{+}{\rm W}^{-}\rightarrow{\rm q}\bar{\rm q}\ell\bar{\nu}_{\ell}$
Efficiency [%]	87.7 $\pm$ 1.1
Signal events	1173 $\pm$28
4-fermion, TGC-dep.	24 $\pm$ 4
4-fermion, TGC-indep.	34 $\pm$ 3
Z $^{0}/\gamma\rightarrow{\rm f}\bar{\rm f}$	48 $\pm$ 5
Two-photon	3 $\pm$ 2
Total Background	111 $\pm$ 8
Total expected	1284 $\pm$ 29
Observed	1246