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 $t\overline{t}$ 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, and the top-quark mass to a precision of 200 (70) MeV, provided that theoretical and experimental systematics are understood. A measurement of $\Delta m_t=200\mathrm{}$ MeV for fixed $M_W$ would constrain a 100 GeV SM Higgs boson mass within about $\pm 2$ GeV, while $\Delta M_W=6\mathrm{}$ MeV for fixed $m_t$ would constrain $m_h$ to about $\pm 10$ GeV.

• Received 18 February 1997

DOI:https://doi.org/10.1103/PhysRevD.56.1714