a $5\sigma$-evidence.

A $95\%\,$C.L. exclusion corresponds to $S$ and $B$ satisfying 1-=0.95. \[eq:excl\] In contrast to the case of discovery, the additional parameter $N$ appears. This is the maximum observed event number up to which the $95\%\,$C.L. exclusion is demanded to hold. For $N=B$ we obtain the central value of the exclusion limit. Repeating the analysis for $N$ at the boundaries of the $1\sigma$ and $2\sigma$ intervals around $B$ then yields the $1\sigma$ and $2\sigma$ probability bands for the exclusion limit.

Inserting $S$ and $B$ as functions of ${\mathcal{L}_{{}^{\int}}}$ and $\sigma_{\rm B}$ according to (\[eq:S\]) and (\[eq:B\]) turns the formulae (\[eq:disc\]) and (\[eq:excl\]) into implicit functions determining ${\mathcal{L}_{{}^{\int}}}({m_{{{\widetilde{\tau}}}_1}})$.

(0.78,0.55) (0.0,0.03) (0.173,0.03) (0.72,0.447)[$\mbox{\small{${\color{green} 10^{-10}}$}}$]{} (0.515,0.447)[$\mbox{\small{${\color{green}10^{-7}}$}}$]{} (0.597,0.447)[$\mbox{\small{${\color{red}10^{-7}\,\,10^{-10}}$}}$]{} (-0.04,0.115) (0.36,-0.006)[$m_{{{\widetilde{\tau}}}_1}\;[$GeV$]$]{} (0.551,0.3233) (0.251,0.2507) (0.203,0.3) (0.087,0.081)[$7{\ensuremath{\,\textnormal{TeV}}}$]{} (0.667,0.081)[$14{\ensuremath{\,\textnormal{TeV}}}$]{}

As signal cross section we use $\sigma_{\rm S}({m_{{{\widetilde{\tau}}}_1}})$ at ${\theta_{{{\widetilde{\tau}}}}}={\theta_{{{\widetilde{\tau}}}}}^{\rm min}$ after applying all cuts mentioned above. The trigger and reconstruction efficiency for single stau candidates can be conservatively estimated to be $80\%$ [@Peter], thus we choose (again conservatively) $\epsilon=0.8^2$. The background cross section $\sigma_\text{B}$ is the di-muon cross section after the preselection cuts. As explained earlier, we consider the values $10^{-10}$ as well as $10^{-7}$ for ${{r_{\beta}}}$. Figure \[fig:lum-num-mass-fix\] shows the luminosity ${\mathcal{L}_{{}^{\int}}}({m_{{{\widetilde{\tau}}}_1}})$ at which a $5\sigma$-discovery 