section.

### Dependence on the stau mass {#dependence-on-the-stau-mass .unnumbered}

To show the dependence on the stau mass ${m_{{{\widetilde{\tau}}}_1}}$ we simulated the DY production in $21$ mass steps from $100{\ensuremath{\,\textnormal{GeV}}}$ to $1000{\ensuremath{\,\textnormal{GeV}}}$, generating $5\times10^{4}$ events for each one and again considering diagrams up to order $\alpha_{\rm s}^2$ (two jets). We obtained the normalization of the total cross section from the corresponding leading-order computation (without jets) from MadEvent, corrected by a constant $K$-factor of $1.35$ [@PhysRevD.57.5871]. This value was found for ${m_{{{\widetilde{\tau}}}_1}}\gtrsim 200{\ensuremath{\,\textnormal{GeV}}}$ considering NLO QCD corrections. Additionally including SUSY QCD contributions at NLO and next-to-leading logarithmic accuracy yields a $K$-factor between roughly $1.29$ and $1.36$ [@1999PhRvL..83.3780B; @Bozzi:2007qr; @Bozzi:2007tea].

(0.65,0.52) (0.0,0.02) (-0.025,0.19) (0.283,0.0)[$m_{{{\widetilde{\tau}}}_1}\;[$GeV$]$]{} (0.375,0.429)[without cuts]{} (0.3368,0.3963)[preselection cuts]{} (0.212,0.3636)[preselection and velocity cuts]{}

Figure \[fig:sigma-mass\] shows the results. The cuts on $\eta$, ${p_\text{T}}$, and $\Delta\mathcal{R}_{{{\widetilde{\tau}}}, {\rm jet}}$ have a minor impact on the data, whereas the velocity cut lowers the signal by about one order of magnitude but with a slightly decreasing tendency when going to very high masses due to the increase of slower staus. The fraction of events passing the velocity cut is $8\%$ at ${m_{{{\widetilde{\tau}}}_1}}=200{\ensuremath{\,\textnormal{GeV}}}$ and about $20\%$ at ${m_{{{\widetilde{\tau}}}_1}}=800{\ensuremath{\,\textnormal{GeV}}}$ (cf. figure \[fig:distau-obs\], top). This is due to the fact that 