Significance Variables

Many particle physics analyses which need to discriminate some background process from a signal ignore event-by-event resolutions of kinematic variables. Adding this information, as is done for missing momentum significance, can only improve the power of existing techniques. We therefore propose the use of significance variables which combine kinematic information with event-by-event resolutions. We begin by giving some explicit examples of constructing optimal significance variables. Then, we consider three applications: new heavy gauge bosons, Higgs to $\tau\tau$, and direct stop squark pair production. We find that significance variables can provide additional discriminating power over the original kinematic variables: $\sim$ 20% improvement over $m_T$ in the case of $H\rightarrow\tau\tau$ case, and $\sim$ 30% impovement over $m_{T2}$ in the case of the direct stop search.