Background Elimination
======================

The actual signal for the process considered in the previous section consists of a hard electron and a hard positron, with substantial missing energy. The SM backgrounds arise from all processes of the form $e^+ e^- 
\to e^+ e^- \nu \bar{\nu}$, where the neutrinos can be of any flavor. At the lowest order, there are 96 Feynman diagrams which give rise to this final state. Some of the principal sub-processes are listed below. $$\begin{aligned}
e^+ e^- & \to & e^\pm W^\mp \nu_e^{\!\!\!\!\!\!(-)} 
          \to e^+ e^- \nu_e \bar{\nu}_e \nonumber \\
e^+ e^- & \to & e^+ e^- Z \to  e^+ e^- (\nu \bar{\nu}) \nonumber \\
e^+ e^- & \to & \nu_e \bar{\nu}_e Z \to  \nu_e \bar{\nu}_e (e^+ e^-) \nonumber \\
e^+ e^- & \to & W^+ W^- \to (e^+ \nu_e) (e^- \bar{\nu}_e) \nonumber \\
e^+ e^- & \to & ZZ \to (e^+ e^-) (\nu \bar{\nu}) \nonumber \\
e^+ e^- & \to & \gamma^*Z \to (e^+ e^-) (\nu \bar{\nu}) \end{aligned}$$ Of course, for every process with real $W/Z$, there will also be many diagrams with off-shell particles. Taken together, all these diagrams constitute a formidable background to the suggested signal. A judiciously chosen set of kinematic cuts, however, enable 