Probing Higgs self-coupling of a classically scale invariant model in $e^{+}{e}^{-}\to Zhh$: Evaluation at physical point

A classically scale invariant extension of the standard model predicts large anomalous Higgs self-interactions. We compute missing contributions in previous studies for probing the Higgs triple coupling of a minimal model using the process $e^{+}{e}^{-}\to Zhh$. Employing a proper order counting, we compute the total and differential cross sections at the leading order, which incorporate the one-loop corrections between zero external momenta and their physical values. Discovery/exclusion potential of a future $e^{+}{e}^{-}$ collider for this model is estimated. We also find a unique feature in the momentum dependence of the Higgs triple vertex for this class of models.