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We explore the sensitivity of directly testing the muon-Higgs coupling at ahigh-energy muon collider. This is strongly motivated if there exists newphysics that is not aligned with the Standard Model Yukawa interactions whichare responsible for the fermion mass generation. We illustrate a few suchexamples for physics beyond the Standard Model. With the accidentally smallvalue of the muon Yukawa coupling and its subtle role in the high-energyproduction of multiple (vector and Higgs) bosons, we show that it is possibleto measure the muon-Higgs coupling to an accuracy of ten percent for a 10 TeVmuon collider and a few percent for a 30 TeV machine by utilizing the threeboson production, potentially sensitive to a new physics scale about $\Lambda\sim$ 30-100 TeV.

Precision test of the muon-Higgs coupling at a high-energy muon collider