Testing CP-Violation in the Scalar Sector at Future $e^{+}{e}^{-}$ Colliders

Abstract

We propose a {\em 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 (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 $h_{1}ZZ,h_{2}ZZ,h_1{h}_{2}Z$ 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 $m_2=40\text{GeV}$ at the Circular Electron-Positron Collider (CEPC) with the integrated luminosity $5{\text{ab}}^{-1}$. We find that the discovery of both $Z{h}_2$ and $h_1{h}_2$ processes at $5\sigma$ level will indicate an $\mathcal{O}(10^{-2})$ $K$ 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 "$p_T$ balance" cut (see \autoref{simu} 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.

17 pages, 4 figures, 2 tables; references updated, more discussions on the details of simulation including the kinematical distribution diagrams added, more discussions about mass dependence added; PRD accepted version

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