摘要
We investigate the discovery potential of multi-TeV muon colliders for a heavy darkZboson ( Z_(\rm D) ) with a mass above 1 TeV through the associated production channelμ⁺μ⁻ → Z_(\rm D)γ . This process enables preciseM_(Z_(\rm D))reconstruction using the photon recoil mass ( m_(\rm recoil) ). Focusing on theZ_(\rm D) → jjXandZ_(\rm D) → e⁺e⁻decay modes, we present strategies for achieving high sensitivity to the kinetic mixing parameterεat 3, 6, and 10 TeV muon colliders with integrated luminosities of 1, 4, and 10 ab ⁻¹respectively, assumingZ_(\rm D)decays exclusively into Standard Model particles. A key innovation is our optimized implementation ofM_(Z_(\rm D)) -dependent cuts onm_(\rm recoil) , which accounts for the energy-dependent detector response. For heavierZ_(\rm D) , the associated photon becomes less energetic, leading to better photon energy resolution and thus enabling more stringentm_(\rm recoil)cuts. This approach enhancesεsensitivity for heavierZ_(\rm D) . Conversely, for lighterZ_(\rm D) , the lower-energy electron pair fromZ_(\rm D) → e⁺e⁻enables tighter cuts on the invariant mass of the electron pair ( mₑₑ ), providing better sensitivity in the lighter mass regime. Combining these complementarym_(\rm recoil) - andmₑₑ -based selections with bothjjXande⁺e⁻channels, we achieveεsensitivity down toO\left{(}{1}{0}⁻³\right{)}{}{a}sM_(Z_(\rm D))approaches√s̅ , substantially surpassing the reach of a 100 TeV proton-proton collider. Even ifZ_(\rm D)decays into dark-sector particles, the recoil mass method remains effective, establishing muon colliders as powerful facilities for exploring heavy dark sectors.