Identification of Lepton Candidates

For every event two lepton candidates are selected. The track in the event which is most consistent with being an electron and the track most consistent with being a muon from the decay of a W boson into a lepton ( ${\rm W}\rightarrow\ell\bar{\nu}_{\ell}$) are taken as the lepton candidates. Some events will obviously not contain a lepton, but a track will still be assigned as a lepton however improbable. This procedure does not require explicit lepton identification and is designed to maximise efficiency. For each track in an event which passes the WW112 track quality requirements, a likelihood function is used to give the probability that the track selected arose from a ${\rm W}\rightarrow{\rm e}\bar{\nu}_{\rm e}$ P(e), or from a ${\rm W}\rightarrow\mu\bar{\nu}_{\mu}$ decay, P($\mu$). The WW112 track quality requirements are:

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Momentum $<$ 100 GeV.

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Transverse momentum $>$ 150 MeV.

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$d_{0}$ $<$ 2 cm.

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$z_{0}$ $<$ 25 cm.

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$\chi ^{2}$ per degree of freedom, in both $r-\phi$ and $z$, less than 100.

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At least half the maximum possible number of CJ hits for a track at the measured value of $\cos\theta$ with an absolute minimum of 20 hits.

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Tracks crossing the anode plane, $7.9^{o}<q.\phi_{\rm CJ}<10.5^{o}$, are required to be well measured, $\sigma_{p}/p<0.5$. Where $q$ is the measured charge of the track and $\phi_{\rm CJ}$ is the local azimuthal angle of the track within the CJ sector.

The variables used in the likelihood function can be split into two groups. Firstly those that represent the probability of the track being due to a lepton, namely the energy loss of the track through the tracking chamber and the number of hits in the hadron calorimeter. The second group are variables that represent the probability that the track came from the decay of a W boson, such as the energy deposited in the electromagnetic calorimeter. Table 5.2 lists all the variables used in the likelihood calculation.

For each variable a probability is calculated from comparison with a reference histogram. There is a reference histogram for each flavour of lepton, these are derived from large samples of Monte Carlo events. To calculate the overall probability for each track, the probabilities for each variable are multiplied together. The track with the highest P(e) is taken as the candidate electron in the ${\rm W}^{+}{\rm W}^{-}\rightarrow{\rm q}\bar{\rm q}{\rm e}\bar{\nu}_{\rm e}$ selection and the track with the highest P($\mu$) is taken as the candidate muon in the ${\rm W}^{+}{\rm W}^{-}\rightarrow{\rm q}\bar{\rm q}\mu\bar{\nu}_{\mu}$ selection. At this stage no events are rejected, so every event will have one electron and one muon candidate.

Table 5.2: Variables used to calculate the likelihood of the electron and muon lepton candidate.

Variable	${\rm W}\rightarrow{\rm e}\bar{\nu}_{\rm e}$	${\rm W}\rightarrow\mu\bar{\nu}_{\mu}$
$p_{\rm lepton}$		$\surd$
E $_{\rm lepton}$	$\surd$	$\surd$
I$_{200}$	$\surd$	$\surd$
E/$p$	$\surd$
$\Delta\phi_{EC/CT}$	$\surd$
${\rm d}E/{\rm d}x$	$\surd$
$X_{\rm GCONV}$	$\surd$
$N^{90}_{\rm blk}$	$\surd$
$N_{\rm HC2}$	$\surd$
$N_{\rm HCAL}$		$\surd$
$N_{\rm MUON}$		$\surd$
$X_{\rm hits/layer}$		$\surd$

The use of this many variables ensures that the identification of the lepton candidate is extremely efficient. Studies using Monte Carlo show that for events where the lepton track passes the WW track quality cuts, the following efficiencies are possible. In 98.1% of the ${\rm W}^{+}{\rm W}^{-}\rightarrow{\rm q}\bar{\rm q}{\rm e}\bar{\nu}_{\rm e}$ events the correct track is identified as the lepton and in 99.1% of the ${\rm W}^{+}{\rm W}^{-}\rightarrow{\rm q}\bar{\rm q}\mu\bar{\nu}_{\mu}$ events the correct track is identified as the lepton.