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We propose a novel method using the $ZZ$-fusion channel and forward muondetection at high-energy muon colliders to address the challenge of the Higgscoupling-width degeneracy. Our approach enables inclusive Higgs ratemeasurement to 0.75% at 10~TeV muon collider, breaking the coupling-widthdegeneracy. Results indicate the potential to refine Higgs coupling tosub-percent levels and estimate its total width within (-0.41%, +2.1%). Keyinsights include the effectiveness of forward muon tagging in signal-backgroundseparation despite broad recoil mass distribution due to muon energyreconstruction and beam energy spread. The study emphasizes the significance ofmuon rapidity coverage up to $|\eta (\mu)|<6$, enhancing measurement precision.Our findings highlight the unique capabilities of high-energy lepton collidersfor model-independent Higgs coupling determination and lay the groundwork forfuture advancements in muon collider technology and Higgs physics research.

Higgs Width and Couplings at High Energy Muon Colliders with Forward Muon Detection