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 $HHVV\ (V=W^\pm,Z)$, 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 centre-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, 0.6\% (0.20\%) for $WWHH$ coupling, and 5.6\% (2.0\%) for $HHH$ coupling.