Precision W-Boson and Higgs Boson Mass Determinations at Muon Colliders

Precise determinations of the masses of the $W$ boson and of the top quark could stringently test the radiative structure of the Standard Model (SM) or provide evidence for new physics. We analyze the excellent prospects at a muon collider for measuring $M_W$ and $m_t$ in the $W^+W^-$ and $ZH$ threshold regions. With an integrated luminosity of 10 (100) fb$^{-1}$, the W-boson mass could be measured to a precision of 20 (6) MeV, provided that theoretical and experimental systematics are understood. A measurement of $\Delta M_W=6$ MeV would constrain the mass of a $\sim 100$ GeV Higgs to about $\pm 10$ GeV. We demonstrate that a measurement at future colliders of the Bjorken process. With an integrated luminosity of $100\fbi$ it is possible to measure the Standard Model Higgs mass to within 45\mev at a $\mu^+\mu^-$ collider for $\mh=100\gev$.