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We consider the capability of a future high energy $e^+ e^-$ collider tosearch for the $Z^\prime$ bosons associated with a $U(1)^\prime$ gaugeextension of the Standard Model. Even for $Z^\prime$ masses well above thecenter of mass energy of the collider, the rates of production of $e^+ e^-$,$\mu^+ \mu^-$, unflavored jets, and $b$-tagged jets can reveal the presence ofvirtual $Z^\prime$ exchange. We consider collider configurations withcenter-of-mass energy 200, 300, and 500 GeV, and show how various classes of$Z^\prime$ model-lines can be probed with $100~{\rm fb}^{-1}$ of integratedluminosity. We find that for order one couplings, $Z^\prime$ masses on theorder of several TeV can be discovered, depending on the collider energy. Ourresults suggest that a 200 GeV collision energy is unlikely to discover any ofthe $Z^\prime$ models we consider that would not have already been visible inlate stages of LHC running, but could still help refine understanding of thecouplings and distinguish between different models. For $e^+ e^-$ collisionenergies of 300 GeV, parameter space beyond the reach of the LHC becomesaccessible.

Sensitivity of a Future High Energy $e^+ e^-$ Collider to $Z^\prime$ Bosons