Selection of ${\rm W}^{+}{\rm W}^{-}\rightarrow{\rm q}\bar{\rm q}\tau\bar{\nu}_{\tau}$ Events

The only events so far categorised as ${\rm W}^{+}{\rm W}^{-}\rightarrow{\rm q}\bar{\rm q}\tau\bar{\nu}_{\tau}$ events are those that passed either the ${\rm W}^{+}{\rm W}^{-}\rightarrow{\rm q}\bar{\rm q}{\rm e}\bar{\nu}_{\rm e}$ or ${\rm W}^{+}{\rm W}^{-}\rightarrow{\rm q}\bar{\rm q}\mu\bar{\nu}_{\mu}$ selection. These amount to only about 30% of the total number of ${\rm W}^{+}{\rm W}^{-}\rightarrow{\rm q}\bar{\rm q}\tau\bar{\nu}_{\tau}$ events. All events that failed both the ${\rm W}^{+}{\rm W}^{-}\rightarrow{\rm q}\bar{\rm q}{\rm e}\bar{\nu}_{\rm e}$ and ${\rm W}^{+}{\rm W}^{-}\rightarrow{\rm q}\bar{\rm q}\mu\bar{\nu}_{\mu}$ selection are now subjected to the ${\rm W}^{+}{\rm W}^{-}\rightarrow{\rm q}\bar{\rm q}\tau\bar{\nu}_{\tau}$ selection. The selection is designed to be sensitive to the four main tau decay channels, namely the electron, the muon, the hadronic one prong and the hadronic three prong, ${\rm W}^{+}{\rm W}^{-}\rightarrow{\rm q}\bar{\rm q}\tau\bar{\nu}_{\tau}\rightarrow{\rm q}\bar{\rm q}\pi^{\pm}\pi^{\pm}\pi^{\mp}\nu_{\tau}\bar{\nu}_{\tau}$.

Table 5.4: Variables used to calculate the likelihood of the tau lepton candidate in the four tau decay channels.

Variable	$\tau\rightarrow{\rm e}$	$\tau\rightarrow\mu$	$\tau\rightarrow1{\rm h}$	$\tau\rightarrow3{\rm h}$
$p_{\rm lepton}$		$\surd$		$\surd$
E $_{\rm lepton}$	$\surd$	$\surd$
E$_{\tau}$			$\surd$
I$_{200}$	$\surd$	$\surd$
I $^{\rm CT}_{200}$			$\surd$	$\surd$
I $_{200-500}$			$\surd$	$\surd$
E/$p$	$\surd$
$\Delta\phi_{EC/CT}$	$\surd$
${\rm dE}/{\rm d}x$	$\surd$
X $_{\rm GCONV}$	$\surd$
N $^{90}_{\rm blk}$	$\surd$
N $_{\rm HC2}$	$\surd$
N $_{\rm HCAL}$		$\surd$
N $_{\rm MUON}$		$\surd$
X $_{\rm hits/layer}$		$\surd$
$\cos\theta_{\ell\vec{\rm p}}$			$\surd$
N $^{\rm lepton-jet}_{\rm CT}$			$\surd$	$\surd$
M$_{\tau}$			$\surd$	$\surd$

The selection proceeds as for the ${\rm W}^{+}{\rm W}^{-}\rightarrow{\rm q}\bar{\rm q}{\rm e}\bar{\nu}_{\rm e}$ and ${\rm W}^{+}{\rm W}^{-}\rightarrow{\rm q}\bar{\rm q}\mu\bar{\nu}_{\mu}$ channels. The identification of the lepton candidate is replaced by the identification of the track most consistent with being from each of the four possible tau decay channels. For the three prong tau decay the combination of three tracks most consistent with being from this process is identified. The variables used in this process are shown in table 5.4. The efficiency of this identification is less than that for the electrons and muons, but still a respectable 79.5% of events are expected to have the correct track(s) identified as the tau.

Now preselection is applied. A list of all the cuts applied in the preselection for each $\tau$ decay channel is shown in table 5.9.

The likelihood selection applied uses the same variables as for the other leptons, but with the addition of more information about the tracks. An event is selected as coming from a certain channel if the relative likelihood is greater than 0.75. Once again, events passing more than one ${\rm W}^{+}{\rm W}^{-}\rightarrow{\rm q}\bar{\rm q}\tau\bar{\nu}_{\tau}$ likelihood selection are subjected to a new likelihood selection using a subset of variables to ensure it enters into the final data set only once. A list of all the variables used in the likelihood selection can be found in table 5.5.