Higgs Pair Productions in the CP-violating Two-Higgs-Doublet Model

The SM-like Higgs pair productions are discussed in the framework of the general CP-violating two-Higgs-doublet model, where we find the CP-violating mixing angles can be related to the Higgs self couplings. Therefore, the future experimental searches for Higgs boson pairs can be constrained by the improved precision of the electric dipole moment measurements. Based on a series constraints of the SM-like Higgs boson signal fits, the perturbative unitarity and stability bounds to the Higgs potential, and the most recent LHC searches for the heavy Higgs bosons, we suggest a set of benchmark models for the future high-energy collider searches for the Higgs pair productions. The $e^+ e^-$ colliders operating at $\sqrt{s}=$ (500 GeV, 1 TeV) are capable of measuring the Higgs cubic self couplings of the benchmark models directly. We also estimate the cross sections of the resonance contributions to the Higgs pair productions for the benchmark models at the future LHC and SppC/Fcc-hh runs.