a function of $\sqrt{\hat{s}}$ for up-type quarks (red dashed line) and down-type quarks (blue dotted line). In each case the ratio is normalized to be one at $\hat{s}\to\infty$. Right: Cross section for direct di-stau production $pp\to Z,\gamma\to {{\widetilde{\tau}}}_1^+{{\widetilde{\tau}}}_1^-$ as a function of the stau mixing angle. The curves are obtained from a MadEvent simulation with ${m_{{{\widetilde{\tau}}}_1}}=500{\ensuremath{\,\textnormal{GeV}}}$ (solid green, normalized to be one at ${\theta_{{{\widetilde{\tau}}}}}=0$) as well as directly from (\[eq:DYcross-section\]) for up-type quarks (red dashed line) and down-type quarks (blue dotted line) for a center-of-mass energy $\sqrt{\hat{s}}=1000{\ensuremath{\,\textnormal{GeV}}}$. The two latter curves are absolutely normalized to be equal to the MadEvent prediction at their intersection point.[]{data-label="fig:theta-stau"}](e-ew-s.eps "fig:")]{} (-0.045,0.185) (0.188,0.0)[$\sqrt{\hat{s}}\;[$GeV$]$]{} (0.5,0.04)[![Left: Ratio between the electromagnetic contribution and the complete electroweak cross section (\[eq:DYcross-section\]) for ${\theta_{{{\widetilde{\tau}}}}}=0$ as a function of $\sqrt{\hat{s}}$ for up-type quarks (red dashed line) and down-type quarks (blue dotted line). In each case the ratio is normalized to be one at $\hat{s}\to\infty$. Right: Cross section for direct di-stau production $pp\to Z,\gamma\to {{\widetilde{\tau}}}_1^+{{\widetilde{\tau}}}_1^-$ as a function of the stau mixing angle. The curves are obtained from a MadEvent simulation with ${m_{{{\widetilde{\tau}}}_1}}=500{\ensuremath{\,\textnormal{GeV}}}$ (solid green, normalized to be one at ${\theta_{{{\widetilde{\tau}}}}}=0$) as well as directly from (\[eq:DYcross-section\]) for up-type quarks (red dashed line) 