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"}](sigma-theta.eps "fig:")]{} (0.46,0.165) (0.715,0.0)[${\theta_{{{\widetilde{\tau}}}}}$]{}

### Dependence on the mixing angle {#dependence-on-the-mixing-angle .unnumbered}

We define the stau mixing matrix via \[\]

\_1\
\_2

=[M]{}\^

\_\
\_

=

\_& \_\
-\_&\_

\_\
\_

\[eq:mixing-def\] and $m_{{{\widetilde{\tau}}}_1}\leq m_{{{\widetilde{\tau}}}_2}$. The dependence of the di-stau cross section on the mixing angle ${\theta_{{{\widetilde{\tau}}}}}$ can be discussed by considering the tree-level parton-level cross section for $q\bar{q} \to Z,\gamma \to {{\widetilde{\tau}}}_i^+{{\widetilde{\tau}}}_j^-$, ( )\^[q]{}\_[ij]{}= , \[eq:DYcross-section\] where g\_[\_i\_j]{}= \[eq:g-stau-def\] and g\_\^[q]{}=, g\_\^[q]{}=. \[eq:g-quark-def\] Here $q$ denotes the flavor of the annihilating quark, while $Q_q$ and $T^3_q$ are its electric charge and the third component of its weak isospin, respectively. Besides, $c_{\text{W}}\equiv\cos{\theta_W}$, $s_{\text{W}}\equiv\sin{\theta_{\text{W}}}$, and $\hat{s}$, $\hat{t}$, $\hat{u}$ are the Mandelstam variables. (Taking into account the width $\Gamma_Z\ll M_Z$ is not vital for the following argumentation.)

A change in ${\theta_{{{\widetilde{\tau}}}}}$ has an impact on $g_{{{\widetilde{\tau}}}_i{{\widetilde{\tau}}}_j}$ only. Thus, it alters the ratio between the three terms in square brackets in , which are the electromagnetic, the weak and the interference terms, respectively. This change is almost independent of the kinematics. The terms in square 