Precision Higgs Boson Mass Determination at Lepton Colliders

We demonstrate that a measurement at future colliders of the Bjorken process $e^{+}{e}^{-}$, ${\mu }^{+}{\mu }^{-}\to \mathrm{ZH}$ in the threshold region can yield a precise determination of the Higgs boson mass. With an integrated luminosity of $100{\mathrm{fb}}^{-1\mathrm{}}$ it is possible to measure the standard model Higgs mass to within 45 MeV (60 MeV) at ${\mu }^{+}{\mu }^{-}\left(e^{+}{e}^{-}\right)$ collider for $m_H=100\mathrm{}\mathrm{GeV}$.