Prospect for measurement of CP-violating parameters of $B_s^0\to \ddot{I}•{\hat{I}}^3$ at the Tera Z factory

Abstract

$b\to s{\hat{I}}^3$ 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 $B_s^0\to \ddot{I}•{\hat{I}}^3$ 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 $B_s^0\to \ddot{I}•{\hat{I}}^3$ decay, accounting for $B_s^0/{\bar{B}}_s^0$ mixing extract the mixing-induced and CP-violating parameters ${\mathcal{A}}_{\ddot{\mathbf{I}}•{\hat{\mathbf{I}}}^3}^{\hat{\mathbf{I}}}”$, ${\mathbf{C}}_{\ddot{\mathbf{I}}•{\hat{\mathbf{I}}}^3}$ and ${\mathbf{S}}_{\ddot{\mathbf{I}}•{\hat{\mathbf{I}}}^3}$. Using central value from LHCb measurement as input, we evaluate the anticipated accuracy of measurements of these parameters. The projected statistical uncertainties are $\ddot{I}{ƒ}_{A_{\ddot{I}•{\hat{I}}^3}^{\hat{I}}”{}^{\text{stat}}}=0.021$, $\ddot{I}{ƒ}_C^{\text{stat}}=0.0092$ and $\ddot{I}{ƒ}_S^{\text{stat}}=0.0096$, and the systematic uncertainties are $\ddot{I}{ƒ}_{A_{\ddot{I}•{\hat{I}}^3}^{\hat{I}}”{}^{\text{syst}}}=0.035$, $\ddot{I}{ƒ}_C^{\text{syst}}=0.0027$ and $\ddot{I}{ƒ}_S^{\text{syst}}=0.0064$. Furthermore, the 1$\ddot{I}ƒ$ sensitivity boundaries for NP in this study are found to be ${\mathcal{A}}_{\ddot{I}•{\hat{I}}^3}^{\hat{I}}”<-0.05$ or ${\mathcal{A}}_{\ddot{I}•{\hat{I}}^3}^{\hat{I}}”>0.15$, ${\mathcal{C}}_{\ddot{I}•{\hat{I}}^3}<-0.02$ or ${\mathcal{C}}_{\ddot{I}•{\hat{I}}^3}>0.04$, and ${\mathcal{S}}_{\ddot{I}•{\hat{I}}^3}<-0.04$ or ${\mathcal{S}}_{\ddot{I}•{\hat{I}}^3}>0.04$. 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.