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Strong Interaction Effects in Stop Pair Production at $e^+ e^-$ Colliders

We discuss perturbative and non-perturbative strong interaction effects in the pair production of stop squarks ($\tilde{t}_1$) at $e^+ e^-$ colliders. Events with an additional hard gluon allow to detect or exclude stop pair production even in scenarios with very small mass splitting between $\tilde{t}_1$ and an invisible lightest supersymmetric particle (LSP). Such events can also help to establish that $\tilde{t}_1$ transforms as a triplet under $SU(3)_C$. We also carefully study non-perturbative $\tilde{t}_1$ fragmentation, which is currently not well understood: not only is the $\tilde{t}_1$ fragmentation function not known very well, but also there are ambiguities in the algorithm employed to model fragmentation. We present numerical results both for CERN LEP-183 and for a proposed future $e^+ e^-$ collider operating at center-of-mass energy $\sqrt{s}=500$ GeV.