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

We consider the capability of a future high energy $e^+ e^-$ collider to search for the $Z^\prime$ bosons associated with a $U(1)^\prime$ gauge extension of the Standard Model. Even for $Z^\prime$ masses well above the center 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 of virtual $Z^\prime$ exchange. We consider collider configurations with center-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 integrated luminosity. We find that for order one couplings, $Z^\prime$ masses on the order of several TeV can be discovered, depending on the collider energy. Our results suggest that a 200 GeV collision energy is unlikely to discover any of the $Z^\prime$ models we consider that would not have already been visible in late stages of LHC running, but could still help refine understanding of the couplings and distinguish between different models. For $e^+ e^-$ collision energies of 300 GeV, parameter space beyond the reach of the LHC becomes accessible.