Relative Likelihood Selection

For events that have passed the initial preselection, a likelihood is given to them that they are a ${\rm W}^{+}{\rm W}^{-}\rightarrow{\rm q}\bar{\rm q}{\rm e}\bar{\nu}_{\rm e}$ event ( ${\rm L}^{{\rm q}\bar{\rm q}{\rm e}\nu}$) or a ${\rm W}^{+}{\rm W}^{-}\rightarrow{\rm q}\bar{\rm q}\mu\bar{\nu}_{\mu}$ event ( ${\rm L}^{{\rm q}\bar{\rm q}\mu\nu}$). A number of variables are looked at to calculate this likelihood. These variables are shown in table 5.3.

Table 5.3: Variables used to calculate the relative likelihood selection of 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.

Variable	${\rm W}^{+}{\rm W}^{-}\rightarrow{\rm q}\bar{\rm q}{\rm e}\bar{\nu}_{\rm e}$	${\rm W}^{+}{\rm W}^{-}\rightarrow{\rm q}\bar{\rm q}\mu\bar{\nu}_{\mu}$
E $_{\rm lepton}$	$\surd$	$\surd$
I$_{200}$	$\surd$	$\surd$
P($\ell$)	$\surd$	$\surd$
$\cos\theta_{\rm mis}$	$\surd$	$\surd$
R $_{\rm vis}$	$\surd$	$\surd$
$\sum P{\rm T}$	$\surd$	$\surd$
$\cos\theta_{\rm lpmis}$	$\surd$	$\surd$
P( $s^{\prime}$)		$\surd$
N $^{\rm lepton-jet}_{\rm CT}$		$\surd$
$\sqrt{s^{\prime}}$	$\surd$	$\surd$

A probability is calculated for each variable by comparing the observed value with expected distributions obtained from Monte Carlo events. The likelihood L $^{{\rm q}\bar{\rm q}\ell\nu}$ is calculated as the product of these probabilities. Using the same approach a likelihood is also calculated for the event being a background ${\rm Z}^{0}/\gamma \rightarrow {\rm q}\bar{\rm q}$ event (L $^{\rm q\bar{\rm q}}$). A relative likelihood is then calculated for the event. For example, the relative likelihood that the event is a ${\rm W}^{+}{\rm W}^{-}\rightarrow{\rm q}\bar{\rm q}{\rm e}\bar{\nu}_{\rm e}$ would be:

$${\cal{L}}^{{\rm q}\bar{\rm q}{\rm e}\nu} = \frac{{\rm L}^{{\rm q}... ...{\rm L}^{{\rm q}\bar{\rm q}{\rm e}\nu} + f \times {\rm L}^{{\rm q}\bar{\rm q}}}$$ (5.1)

Where $f$ is the expected ratio of preselected background to signal cross-sections calculated from Monte Carlo. Events with ${\cal{L}}^{{\rm q}\bar{\rm q}{\rm e}\nu} > 0.5$ are selected as ${\rm W}^{+}{\rm W}^{-}\rightarrow{\rm q}\bar{\rm q}{\rm e}\bar{\nu}_{\rm e}$ events and those with ${\cal{L}}^{{\rm q}\bar{\rm q}\mu\nu} > 0.5$ are selected as ${\rm W}^{+}{\rm W}^{-}\rightarrow{\rm q}\bar{\rm q}\mu\bar{\nu}_{\mu}$ events. Events can be selected as both of these. The combination of preselection and likelihood selection rejects over 99.5% of the ${\rm Z}^{0}/\gamma \rightarrow {\rm q}\bar{\rm q}$ background and is approximately 90% efficient for ${\rm W}^{+}{\rm W}^{-}\rightarrow{\rm q}\bar{\rm q}{\rm e}\bar{\nu}_{\rm e}$ and ${\rm W}^{+}{\rm W}^{-}\rightarrow{\rm q}\bar{\rm q}\mu\bar{\nu}_{\mu}$ events.