Event Categorisation

The preselection and likelihood selection are optimised to separate the ${\rm W}^{+}{\rm W}^{-}\rightarrow{\rm q}\bar{\rm q}{\rm e}\bar{\nu}_{\rm e}$ and ${\rm W}^{+}{\rm W}^{-}\rightarrow{\rm q}\bar{\rm q}\mu\bar{\nu}_{\mu}$ events from the background ${\rm Z}^{0}/\gamma \rightarrow {\rm q}\bar{\rm q}$ events. As a result of the relative likelihood selection, events are classified as ${\rm W}^{+}{\rm W}^{-}\rightarrow{\rm q}\bar{\rm q}{\rm e}\bar{\nu}_{\rm e}$ or ${\rm W}^{+}{\rm W}^{-}\rightarrow{\rm q}\bar{\rm q}\mu\bar{\nu}_{\mu}$ events, or as both. For the ambiguous events, a relative likelihood is constructed to discriminate between the two possible cases, so all events can only be put in just one category.

However, approximately 30% of the events will actually be ${\rm W}^{+}{\rm W}^{-}\rightarrow{\rm q}\bar{\rm q}\tau\bar{\nu}_{\tau}$ events. So all events passing the ${\rm W}^{+}{\rm W}^{-}\rightarrow{\rm q}\bar{\rm q}{\rm e}\bar{\nu}_{\rm e}$ selection are reclassified as ${\rm W}^{+}{\rm W}^{-}\rightarrow{\rm q}\bar{\rm q}{\rm e}\bar{\nu}_{\rm e}$ or ${\rm W}^{+}{\rm W}^{-}\rightarrow{\rm q}\bar{\rm q}\tau\bar{\nu}_{\tau}$ events. A similar procedure is undertaken for the events passing the ${\rm W}^{+}{\rm W}^{-}\rightarrow{\rm q}\bar{\rm q}\mu\bar{\nu}_{\mu}$ selection.

New relative likelihoods are calculated. The predominant ${\rm W}^{+}{\rm W}^{-}\rightarrow{\rm q}\bar{\rm q}\tau\bar{\nu}_{\tau}$ events that are selected as ${\rm W}^{+}{\rm W}^{-}\rightarrow{\rm q}\bar{\rm q}{\rm e}\bar{\nu}_{\rm e}$ events are where the tau lepton decays into an electron, ${\rm W}^{+}{\rm W}^{-}\rightarrow{\rm q}\bar{\rm q}\tau\bar{\nu}_{\tau}\rightarrow{\rm q}\bar{\rm q}{\rm e}\bar{\nu}_{\rm e}\nu_{\tau}\bar{\nu}_{\tau}$, or a one prong hadronic state, ${\rm W}^{+}{\rm W}^{-}\rightarrow{\rm q}\bar{\rm q}\tau\bar{\nu}_{\tau}\rightarrow{\rm q}\bar{\rm q}\pi^{\pm}n\pi^{0}\nu_{\tau}\bar{\nu}_{\tau}$. Likelihoods are calculated for the event being from each of these two processes using the same variables as before. Relative likelihoods are then formed to discriminate between the ${\rm W}^{+}{\rm W}^{-}\rightarrow{\rm q}\bar{\rm q}{\rm e}\bar{\nu}_{\rm e}$ and ${\rm W}^{+}{\rm W}^{-}\rightarrow{\rm q}\bar{\rm q}\tau\bar{\nu}_{\tau}$ events. An example of the relative likelihood between ${\rm W}^{+}{\rm W}^{-}\rightarrow{\rm q}\bar{\rm q}{\rm e}\bar{\nu}_{\rm e}$ and ${\rm W}^{+}{\rm W}^{-}\rightarrow{\rm q}\bar{\rm q}\tau\bar{\nu}_{\tau}\rightarrow{\rm q}\bar{\rm q}{\rm e}\bar{\nu}_{\rm e}\nu_{\tau}\bar{\nu}_{\tau}$ is shown below:

$${\cal{L}}^{{\rm q}\bar{\rm q}{\rm e}\bar{\nu}_{\rm e}\nu_{\tau}\b... ...u}_{\rm e}\nu_{\tau}\bar{\nu}_{\tau}} + {\rm L}^{{\rm q}\bar{\rm q}{\rm e}\nu}}$$ (5.2)

If any of these relative likelihoods are greater than 0.5 the event is categorised as a ${\rm W}^{+}{\rm W}^{-}\rightarrow{\rm q}\bar{\rm q}\tau\bar{\nu}_{\tau}$ event. A similar procedure is applied to the ${\rm W}^{+}{\rm W}^{-}\rightarrow{\rm q}\bar{\rm q}\mu\bar{\nu}_{\mu}$ events to separate out the ${\rm W}^{+}{\rm W}^{-}\rightarrow{\rm q}\bar{\rm q}\tau\bar{\nu}_{\tau}\rightarrow{\rm q}\bar{\rm q}{\mu}\bar{\nu}_{\mu}\nu_{\tau}\bar{\nu}_{\tau}$ and ${\rm W}^{+}{\rm W}^{-}\rightarrow{\rm q}\bar{\rm q}\tau\bar{\nu}_{\tau}\rightarrow{\rm q}\bar{\rm q}\pi^{\pm}n\pi^{0}\nu_{\tau}\bar{\nu}_{\tau}$ events from them.