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Prospect for measurement of CP-violating parameters of $B_s^0 \to ϕγ$ at the Tera Z factory

$b \to sγ$ transition is a critical flavor-changing neutral current (FCNC) process that could be used to probe CP violation (CPV) and new physics (NP). We quantify the anticipated precision for measuring $B_s^0 \to ϕγ$ at the CEPC Z pole operation, showing that the relative statistical uncertainty could be as low as 0.16\%, improved by approximately two orders of magnitude compared to existing measurements. Additionally, we perform a time-dependent analysis of the $B_s^0 \to ϕγ$ decay, accounting for $B_s^0/\bar{B}_s^0$ mixing extract the mixing-induced and CP-violating parameters $\boldsymbol{\mathcal{A}_{ϕγ}^Δ}$, $\boldsymbol{C_{ϕγ}}$ and $\boldsymbol{S_{ϕγ}}$. Using central value from LHCb measurement as input, we evaluate the anticipated accuracy of measurements of these parameters. The projected statistical uncertainties are $σ_{A_{ϕγ}^Δ{}^{\text{stat}}} = 0.021$, $σ_C^{\text{stat}} = 0.0092$ and $σ_S^{\text{stat}} = 0.0096$, and the systematic uncertainties are $σ_{A_{ϕγ}^Δ{}^{\text{syst}}} = 0.035$, $σ_C^{\text{syst}} = 0.0027$ and $σ_S^{\text{syst}} = 0.0064$. Furthermore, the 1$σ$ sensitivity boundaries for NP in this study are found to be $\mathcal{A}_{ϕγ}^Δ< -0.05$ or $\mathcal{A}_{ϕγ}^Δ> 0.15$, $\mathcal{C}_{ϕγ} < -0.02$ or $\mathcal{C}_{ϕγ} > 0.04$, and $\mathcal{S}_{ϕγ} < -0.04$ or $\mathcal{S}_{ϕγ} > 0.04$. We also conduct a relevant detector optimization study by establishing the correlation between the anticipated precision and the intrinsic resolution of the ECAL, as well as the performance of the PID system.