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