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

TL;DR

This study evaluates the potential for precise measurement of CP-violating parameters in the $B_s^0 o \,\phi\gamma$ decay at the Tera Z factory, highlighting significant improvements over current measurements and exploring detector optimization.

Contribution

It provides projected statistical and systematic uncertainties for CP violation parameters at the Tera Z factory, including detector optimization insights.

Findings

Projected statistical uncertainty for $A_{\phi\gamma}^\Delta$ is 0.021.

Projected statistical uncertainties for $C_{\phi\gamma}$ and $S_{\phi\gamma}$ are approximately 0.0092 and 0.0096.

Sensitivity boundaries for new physics are established for the CP-violating parameters.

Abstract

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