Testing CP violation in the scalar sector at future e+e- colliders

We propose a model-independent method to test CP violation in the scalar sector through measuring the inclusive cross sections of e(+)e(-). -> Zh(1), Zh(2), h(1) h(2) processes with the recoil mass technique, where h(1), h(2) stand for the 125 GeV standard model-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 h(1) ZZ, h(2) ZZ, h(1) h(2)Z 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 m(2) = 40 GeV at the Circular Electron-Positron Collider (CEPC) with the integrated luminosity 5 ab(-1). We find that the discovery of both Zh(2) and h(1) h(2) processes at 5 sigma level indicates an O(10(-2)) K value that 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 p(T) balance cut (see Sec. II B for the definition). Lastly we point out that K not equal 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.