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

• Received 28 January 2024
• Accepted 8 March 2024

DOI:https://doi.org/10.1103/PhysRevD.109.073009

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Published by the American Physical Society