We evaluate the $e^- e^+ to e^- e^+ +h$ process through the $ZZ$ fusion channel at the International Linear Collider (ILC) operating at $500$ GeV and $1$ TeV center of mass energies. We perform realistic simulations on the signal process and background processes. With judicious kinematic cuts, we find that the inclusive cross section can be measured to $2.9%$ after combining the $500$ GeV at $500 text{fb}^{-1}$ and $1$ TeV at $1~ text{ab}^{-1}$ runs. A multivariate log-likelihood analysis further improves the precision of the cross section measurement to $2.3%$. We discuss the overall improvement to model-independent Higgs width and coupling determinations and demonstrate the use of different channels in distinguishing new physics effects in Higgs physics. Our study demonstrates the importance of the $ZZ$ fusion channel to Higgs precision physics, which has often been neglected in the literature.
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