Potential Precision on Higgs Couplings and Total Width at the ILC

We outline a systematic approach to the determination of the Standard Model-like Higgs boson total width and measurable coupling parameters in a model-independent manner at the International Linear Collider (ILC) and illustrate the complementarity for operating the ILC at $250$ GeV near the $Zh$ threshold and at $500$ GeV and $1$ TeV utilizing the $WW, ZZ$ fusion processes. We perform detailed simulations for an important contributing channel to the coupling determination and for invisible decays. Without model assumptions, and combining the information for the coupling ratios from the LHC, the total width can be determined to an accuracy of about $6$, and the couplings for the observable channels can be measured to the $(3-5)$ level at 250 GeV, reaching $(1-3)$ level including the 500 GeV results, with further improvements possible with a $1$ TeV run. The best precision for the branching fraction measurement of the Higgs to invisible modes can be reached at $0.5-0.7$ around the $Zh$ threshold. Further studies from $ZZ$ fusion at higher energies may provide significant improvement for the measurements. With modest theory assumptions, the width and coupling determinations can be further improved to the percent or sub-percent level.