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

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