Electroweak couplings of the Higgs boson at a multi-TeV muon collider

We estimate the expected precision at a multi-TeV muon collider for measuring the Higgs boson couplings with electroweak gauge bosons, $HVV$ and HHVV(V=W^±,Z), as well as the trilinear Higgs self-coupling $HHH$. At very high energies both single and double Higgs productions rely on the vector-boson fusion (VBF) topology. The outgoing remnant particles have a strong tendency to stay in the very forward region, leading to the configuration of the ``inclusive process'' and making it difficult to isolate $ZZ$ fusion events from the $WW$ fusion. In the single Higgs channel, we perform a maximum likelihood analysis on $HWW$ and $HZZ$ couplings using two categories: the inclusive Higgs production and the 1-muon exclusive signal. In the double Higgs channel, we consider the inclusive production and study the interplay of the trilinear $HHH$ and the quartic $VVHH$ couplings, by utilizing kinematic information in the invariant mass spectrum. We find that at a center-of-mass energy of 10 TeV (30 TeV) with an integrated luminosity of 10 ab^-1 (90 ab^-1), one may reach a 95% confidence level sensitivity of 0.073% (0.023%) for $WWH$ coupling, 0.61% (0.21%) for $ZZH$ coupling, 0.62% (0.20%) for $WWHH$ coupling, and 5.6% (2.0%) for $HHH$ coupling. For dim-6 operators contributing to the processes, these sensitivities could probe the new physics scale Λ in the order of 1--10 (2--20) TeV at a 10 TeV (30 TeV) muon collider.