Probing a heavy dark Z boson at multi-TeV muon colliders: Leveraging the optimized recoil mass technique

We investigate the discovery potential of multi-TeV muon colliders for a heavy dark Z boson ( Z D ) with a mass above 1 TeV, via the associated production process μ + μ − → Z D γ . This process enables precise reconstruction of M Z D through the photon recoil mass ( m recoil ). Focusing on the Z D → j j X and Z D → e + e − decay modes, we present strategies to achieve high sensitivity to the kinetic mixing parameter ϵ at 3, 6, and 10 TeV muon colliders with integrated luminosities of 1, 4, and 10 ab − 1 , respectively, assuming that Z D decays exclusively into Standard Model particles. We apply mass-dependent cuts on m recoil and m e e to account for the energy-dependent detector response. For heavier M Z D , the associated photon becomes less energetic, leading to better photon energy resolution and enabling more stringent m recoil cuts. Conversely, for lighter M Z D , the lower-energy electron pair from Z D → e + e − allows tighter invariant mass ( m e e ) cuts. By combining these complementary m recoil - and m e e -based selections across both the j j X and e + e − channels, we achieve sensitivity to ϵ down to O ( 10 −