Selection of ${\rm q}\bar{\rm q}\ell\bar{\nu}_{\ell}$ Events

This selection of events is based on that used by OPAL at the lower centre-of-mass energies of 172 GeV and 183 GeV, described in detail in [94,95]. Due to the higher energy, a number of the cuts have slightly changed, but the basic structure remains the same.

Firstly, it should be noted that only events that fail the $\ell^{+}\nu_{\ell}\ell^{\prime -}\bar{\nu}_{\ell^{\prime}}$ selection [66] are considered as possible ${\rm q}\bar{\rm q}\ell\bar{\nu}_{\ell}$ events. Also the full ${\rm q}\bar{\rm q}\tau\bar{\nu}_{\tau}$ selection is only applied to events that have already failed the ${\rm q}\bar{\rm q}{\rm e}\bar{\nu}_{\rm e}$ and ${\rm q}\bar{\rm q}\mu\bar{\nu}_{\mu}$ selection.

The selection of the ${\rm q}\bar{\rm q}{\rm e}\bar{\nu}_{\rm e}$ and ${\rm q}\bar{\rm q}\mu\bar{\nu}_{\mu}$ events proceeds in four stages:

$\bullet$ Identification of the candidate lepton.

$\bullet$ Preselection.

$\bullet$ Relative likelihood selection.

$\bullet$ Event Categorisation.

This selection will select some ${\rm q}\bar{\rm q}\tau\bar{\nu}_{\tau}$ events as ${\rm q}\bar{\rm q}{\rm e}\bar{\nu}_{\rm e}$ or ${\rm q}\bar{\rm q}\mu\bar{\nu}_{\mu}$ events. These are separated out in the event categorisation section. Below, each of these stages is described in detail. Any events not selected as ${\rm q}\bar{\rm q}{\rm e}\bar{\nu}_{\rm e}$ and ${\rm q}\bar{\rm q}\mu\bar{\nu}_{\mu}$ are then passed through the ${\rm q}\bar{\rm q}\tau\bar{\nu}_{\tau}$ selection, which is discussed later in this section.

For the preselection and likelihood selection a number of variables are used, before going on to discuss how these processes proceed, these variables are defined below:

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$d_{0}$ $r-\phi$ impact parameter.

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$z_{0}$ $z$ impact parameter.

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P($\ell$), the lepton identification probability for the candidate lepton track. For example P(e) is the electron identification probability and P($\mu$) is the muon identification probability.

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E $_{\rm lepton}$, the energy of the lepton candidate. For the electron this is calculated using the electromagnetic calorimeter energy. For the muons the track momentum is used.

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$p_{\rm lepton}$, the momentum of the lepton track. For the three prong tau decay it is the sum of the momenta of the three tracks.

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I$_{200}$, the sum of the lepton candidate track momentum and ECAL cluster energy within a 200 mrad cone about the candidate track (excluding clusters associated with the candidate track).

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E/$p$, the ratio of the energy of the associated ECAL clusters to the track momentum.

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$\Delta\phi_{\rm EC/CT}$, difference between the $\phi$ measurement from the track and from the associated ECAL cluster.

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$\frac{\rm dE}{\rm dx}$, the energy loss of the particle in the tracking chamber.

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X $_{\rm GCONV}$, the output of the IDGCON conversion finder which checks if the track is compatible with an electron or positron originating from a gamma conversion.

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N $^{90}_{\rm blk}$, the number of blocks containing 90% of the ECAL cluster energy.

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N $_{\rm HC2}$, the number of layers with hits in the first two layers of an associated hadron calorimeter cluster.

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N $_{\rm HCAL}$, the number of HCAL layers hit in an associated HCAL cluster.

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N $_{\rm muon}$, the number of muon hits associated with track.

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X $_{\rm hits/layer}$, the number of hits in the hadron calorimeter divided by the number of layers with hits.

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$\cos\theta_{\rm lpmis}$, the cosine of the angle between the lepton track and the missing momentum vector.

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$\sqrt{s^{\prime}}$, the reconstructed invariant mass $s^{\prime}$.

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R $_{\rm vis}$, the visible energy of the event scaled by $\sqrt{s}$.

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N$_{\rm CT}$, the number of tracks in the central tracking chamber which passed the WW quality cuts.

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N $^{\rm MIN}_{\rm CT}$, the minimum number of tracks in a jet when the event (including the lepton candidate) is forced into three jets.

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N$_{\rm EC}$, the number of electromagnetic calorimeter clusters.

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R $_{\rm shw}$, the total ECAL energy scaled to $\sqrt{s}$.

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E$_{\rm FD}$, the energy in the calorimeter of the low angle detectors.

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E$_{\gamma}$, the energy of the highest energy isolated photon.

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$\vert\vec{\rm p}\vert$, the scalar momentum of the lepton.

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P( $s^{\prime}$), the probability from a kinematic fit which estimates the reconstructed invariant mass of the event, $\sqrt{s^{\prime}}$.

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$\cos\theta_{\rm mis}$, the cosine of the angle the missing momentum vector makes with the beam axis.

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$\sum{\rm P_{t}}$, the transverse momentum of the event relative to the beam axis, calculated using tracks, ECAL clusters and HCAL clusters.

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N $^{\rm lepton-jet}_{\rm CT}$, the number of tracks in the jet containing the lepton when the event (including lepton candidate) is forced into three jets.

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E$_{\tau}$, the sum of the candidate track momentum and energies of the ECAL clusters within a 200 mrad cone about the candidate track (not including clusters associated with the candidate track).

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I $^{\rm CT}_{200}$, the sum of the track momentum of all the tracks within a 200 mrad isolation cone.

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I $_{200-500}$, the sum of the track momentum and ECAL energy of all the tracks and ECAL clusters within a 200-500 mrad isolation annulus around the candidate track.

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$\cos\theta_{\ell\vec{\rm p}}$, the cosine of the angle between the track momentum and the missing momentum vector.

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M$_{\tau}$, the invariant mass calculated from the track momentum and energies of ECAL clusters within a 200 mrad cone about the candidate track.

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$\cos\theta_{\ell}$, cosine of the polar angle of the lepton candidate.

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E$_{\rm qq}$, energy of the jet-jet system.

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y$_{23}$, the y-cut value for the transition between two and three jets.

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$\cos\theta_{\ell,({\rm jet})}$, cosine between the lepton and the nearest jet axis.