Relation of S/sqrt(B) and the limit on mu

Bottom line: limit on mu scales as one over S/sqrt{B} ie: sqrt{B}/S

We know \[\frac{S}{\sqrt{B}\] and want to determine the corresponding expected stat-only limit on mu Assume, the background is well modelled and we do not have significant sensitivity to signal ( \(D \sim B\)) .

We are Interested in the stat only limlit so we will ignore \(\sigma_B\) and \(\sigma_S\) .

The fitted signal is:

\(S = D - B \sim 0\) with \(\sigma_S = \sqrt{D} \sim \sqrt{B}\)

The fitted mu is

\[\mu = \frac{D - B}{S}\] with \[\sigma_\mu = \frac{\sqrt{B}}{S}\]

The 95% CL on \(\mu\) is \(\sim 2 \sigma_\mu\) or \(2 \times \frac{\sqrt{B}}{S}\)