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Consequences of non-standard Higgs couplings in the final-state distributionsof the process $e^+_{}e^-_{} \to ZHH$ are studied. We derive an analyticexpression for the differential cross section, which has in the most generalcase 9 non-zero functions. These functions are the coefficients of 9 angularterms, depend on the Higgs couplings, and can be experimentally measured asobservables. Symmetry properties of these 9 functions are carefully discussed,and they are divided into 4 categories under CP and $\mathrm{CP\tilde{T}}$. Therelations between our observables and the observables which exist in theliterature are also clarified. We numerically study the dependence of ourobservables on the parameters in an effective Lagrangian for the Higgscouplings. It is shown that these new observables depend on most of theeffective Lagrangian parameters in different ways from the total cross section.A benefit from longitudinally polarized $e^+_{}e^-_{}$ beams is also discussed.

A set of new observables in the process $e^+_{}e^-_{}\to ZHH$