We propose a model-independent method to test $CP$ violation in the scalar sector through measuring the inclusive cross sections of $e^{+}{e}^{-}\to Z{h}_1,Z{h}_2,h_1{h}_2$ 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 $m_2=40\mathrm{GeV}$ at the Circular Electron-Positron Collider (CEPC) with the integrated luminosity $5{\mathrm{ab}}^{-1}$. We find that the discovery of both $Z{h}_2$ and $h_1{h}_2$ processes at $5\sigma$ level indicates an $\mathcal{O}({10}^{-2})$ $K$ 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 $K\ne 0$ 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.

• Received 7 December 2016

DOI:https://doi.org/10.1103/PhysRevD.95.035015