Confidence Level Calculations for $H\rightarrow W^+W^- \rightarrow l^{+}l^{-}\sla{p_{T}}$ for $115<M_H<130\,\gev$ Using Vector Boson Fusion

This note considers three measures of sensitivity used to anticipate the statistical significance of an observation of the Higgs boson at the LHC with the ATLAS detector. It is demonstrated that the heuristic $s/\sqrt{b}$ systematically overestimates the sensitivity and results in qualitatively different optimization conditions for the analysis of $H\rightarrow W^+W^- \rightarrow l^{+}l^{-}\sla{p_{T}}$ for $115<M_H<130\,\gev$ using Vector Boson Fusion (VBF).