Testing CP-Violation in the Scalar Sector at Future e+e- Colliders

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We propose a model-independent method to test CP-violation in the scalar sector through measuring the inclusive cross sections of e+e-→ Zh₁,Zh₂,h₁h₂ processes with the recoil mass technique, where h₁, h₂ stand for the 125 GeV standard model (SM) like Higgs boson and a new lighter scalar respectively. This method effectively measures a quantity K proportional to the product of the three couplings of h₁ZZ,h₂ZZ,h₁h₂Z vertices. The value of K encodes a part of information about CP-violation in the scalar sector. We simulate the signal and backgrounds for the processes mentioned above with m₂=40GeV at the Circular Electron-Positron Collider (CEPC) with the integrated luminosity 5ab⁻¹. We find that the discovery of both Zh₂ and h₁h₂ processes at 5σ level will indicate an O(10⁻²) K value which can be measured to 16% precision. The method is applied to the weakly-coupled Lee model in which CP-violation can be tested either before or after utilizing a "pₜ balance" cut (see simu for the definition). Lastly we point out that K≠ 0 is a sufficient but not a necessary condition for the existence of CP-violation in the scalar sector, namely K = 0 does not imply CP conservation in the scalar sector.