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The CP violating phase $\phi_s$, the $B_s$ decay width and the decay widthdifference are sensitive probe to new physics and can constrain the heavy quarkexpansion theory. The potential for the measurement at future $Z$ factories isstudied. It is found that operating at Tera-$Z$ mode, the expected precisioncan reach: $\sigma(\phi_s) = 4.3~\mathrm{mrad}$, $\sigma(\Delta\Gamma_s) =0.24~\mathrm{ns^{-1}}$ and $\sigma(\Gamma_s) = 0.072~\mathrm{ns^{-1}}$. Theprecision of $\phi_s$ is competitive with the expected resolution that could beachieved by LHCb at High-Luminosity Large Hadron Collider (HL-LHC). Theresolution is only 30\% larger than the expected resolution at LHCb at HL-LHC.If operating at 10-Tera-$Z$ mode, the resolution of $\phi_s$ can be measured at41\% of the resolution of LHCb at HL-LHC. The measurement of $\Gamma_s$ and$\Delta\Gamma_s$ cannot benefit from the excellent time resolution and taggingpower of the future $Z$-factories. Only operating at 10-Tera-$Z$ mode, can the$\Gamma_s$ and $\Delta\Gamma_s$ reach an 18\% larger resolution than theexpected resolution of LHCb at HL-LHC.

Prospect for measurement of CP-violation phase $\phi_s$ study in the $B_s\rightarrow J/\Psi\phi$ channel at future $Z$ factory