New physics close to the electroweak scale is well motivated by a number of theoretical arguments. However, colliders, most notably the Large Hadron Collider (LHC), have failed to deliver evidence for physics beyond the Standard Model. One possibility for how new electroweak-scale particles could have evaded detection so far is if they carry only electroweak charge, i.e. are color neutral. Future $e^+e^-$ colliders are prime tools to study such new physics. Here, we investigate the sensitivity of $e^+e^-$ colliders to scalar partners of the charged leptons, known as sleptons in supersymmetric extensions of the Standard Model. In order to allow such scalar lepton partners to decay, we consider models with an additional neutral fermion, which in supersymmetric models corresponds to a neutralino. We demonstrate that future $e^+e^-$ colliders would be able to probe most of the kinematically accessible parameter space, i.e. where the mass of the scalar lepton partner is less than half of the colliders center-of-mass energy, with only a few days of data. Besides constraining more general models, this would allow to probe some well motivated dark matter scenarios in the Minimal Supersymmetric Standard Model, in particular the incredible bulk and stau co-annihilation scenarios.
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