Determining the $\mathit{t}\overline{t}$ and $\mathit{ZZ}$ Couplings of a Neutral Higgs Boson of Arbitrary $\mathit{CP}$ Nature at the Next Linear Collider

The optimal procedure for extracting the coefficients of different components of an observable which takes the form of unknown coefficients times functions of known form is developed. When applied to $e^{+}{e}^{-}\to t\overline{t}+$ Higgs production at $\sqrt{s}=1\mathrm{}$ TeV and integrated luminosity times efficiency of $50{\mathrm{fb}}^{-1\mathrm{}}$, we find that the $t\overline{t}\to \mathrm{Higgs}\mathrm{CP}$-even and CP-odd couplings and, to a lesser extent, the $\mathrm{ZZ}\to \mathrm{Higgs}$ (CP-even) coupling can be extracted with reasonable errors. Typically, a standard-model-like CP-even Higgs boson can be distinguished from a purely CP-odd Higgs boson at a high level of statistical significance, and vice versa.