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Vector boson fusion at multi-TeV muon colliders

High-energy lepton colliders with a centre-of-mass energy in the multi-TeV range are currently considered among the most challenging and far-reaching future accelerator projects. Studies performed so far have mostly focused on the reach for new phenomena in lepton-antilepton annihilation channels. In this work we observe that starting from collider energies of a few TeV, electroweak (EW) vector boson fusion/scattering (VBF) at lepton colliders becomes the dominant production mode for all Standard Model processes relevant to studying the EW sector. In many cases we find that this also holds for new physics. We quantify the size and the growth of VBF cross sections with collider energy for a number of SM and new physics processes. By considering luminosity scenarios achievable at a muon collider, we conclude that such a machine would effectively be a "high-luminosity weak boson collider," and subsequently offer a wide range of opportunities to precisely measure EW and Higgs coupling as well as to discover new particles.