${{r_{\beta}}}=10^{-14}$ could be achievable.[^2] However, for ${{r_{\beta}}}=10^{-14}$, the relevant background appears only at very high luminosities, when pile-up from different bunch crossings becomes relevant. This fact might lower the background rejection with respect to the naïve expectation of ${{r_{\beta}}}=10^{-14}$. To our knowledge, currently no quantitative study exists about this issue. In any case, we shall see later that a sufficient background rejection (which enables a three-event exclusion over the whole considered region for ${m_{{{\widetilde{\tau}}}_1}}$) can already be achieved with ${{r_{\beta}}}\simeq10^{-10}$. Thus, using this value is both sufficient and conservative. To show the effect of a looser background rejection we will also display the results under the pessimistic assumption that we do not gain anything by requiring *two* stau candidates, hence applying ${{r_{\beta}}}=10^{-7}$.

Following these considerations, we will apply the cuts $0.6 < \beta < 0.8$ on the signal events in order to ensure both a working ToF measurement and a sufficient background rejection.

Signal {#sec:staumixing}
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The direct stau production via DY only involves two parameters of the more than 100 free MSSM parameters, the stau mass ${m_{{{\widetilde{\tau}}}_1}}$ and the mixing angle ${\theta_{{{\widetilde{\tau}}}}}$.

(0.91,0.45) (0.0,0.042)[![Left: Ratio between the electromagnetic contribution and the complete electroweak cross section (\[eq:DYcross-section\]) for ${\theta_{{{\widetilde{\tau}}}}}=0$ as 