This paper presents a full simulation study of the measurement of the production cross section ($sigma_{mathrm{ZH}}$) of the Higgsstrahlung process $mathrm{e^{+}e^{-}rightarrow ZH}$ and the Higgs boson mass ($M_{mathrm{H}}$) at the International Linear Collider (ILC), using events in which a Higgs boson recoils against a Z boson decaying into a pair of muons or electrons. The analysis is carried out for three center-of-mass energies $sqrt{s}$ = 250, 350, and 500 GeV, and two beam polarizations $mathrm{e_{L}^{-}e_{R}^{+}}$ and $mathrm{e_{R}^{-}e_{L}^{+}}$, for which the polarizations of $mathrm{e^{-}}$ and $mathrm{e^{+}}$ are $left(Pmathrm{e^{-}},Pmathrm{e^{+}}right)$ =($-$80%, +30%) and (+80%, $-$30%), respectively. Assuming an integrated luminosity of 250 $mathrm{fb^{-1}}$ for each beam polarization at $sqrt{s}$ = 250 GeV, where the best lepton momentum resolution is obtainable, $sigma_{mathrm{ZH}}$ and $M_{mathrm{H}}$ can be determined with a precision of 2.5% and 37 MeV for $mathrm{e_{L}^{-}e_{R}^{+}}$ and 2.9% and 41 MeV for $mathrm{e_{R}^{-}e_{L}^{+}}$, respectively. Regarding a 20 year ILC physics program, the expected precisions for the $mathrm{HZZ}$ coupling and $M_{mathrm{H}}$ are estimated to be 0.4% and 14 MeV, respectively. The event selection is designed to optimize the precisions of $sigma_{mathrm{ZH}}$ and $M_{mathrm{H}}$ while minimizing the bias on the measured $sigma_{mathrm{ZH}}$ due to discrepancy in signal efficiencies among Higgs decay modes. For the first time, model independence has been demonstrated to a sub-percent level for the $sigma_{mathrm{ZH}}$ measurement at each of the three center-of-mass energies. The results presented show the impact of center-of-mass energy and beam polarization on the evaluated precisons and serve as a benchmark for the planning of the ILC run scenario.
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