Prospect for measurement of the CP-violating phase ${\varphi }_s$ in the $B_s\to J/\psi \varphi$ channel at a future Z factory

Abstract

The CP-violating phase ${\varphi }_s$, the \Bs decay width (${\Gamma }_s$), and the \Bs decay width difference ($\Delta {\Gamma }_s$) are sensitive probes to new physics and can constrain the heavy quark expansion theory. The potential for the measurement at future $Z$ factories is studied in this manuscript. It is found that operating at Tera-$Z$ mode, the expected precision can reach: $\sigma ({\varphi }_s)=4.6\mathrm{mrad}$, $\sigma (\Delta {\Gamma }_s)=2.4\mathrm{n}{\mathrm{s}}^{-1}$ and $\sigma ({\Gamma }_s)=0.72\mathrm{n}{\mathrm{s}}^{-1}$. The precision of ${\varphi }_s$ is 40\% larger than the expected precision with the LHCb experiment at HL-LHC. If operating at 10-Tera-$Z$ mode, the precision of ${\varphi }_s$ can be measured at 45\% of the precision obtained from the LHCb experiment at HL-LHC. However, the measurement of ${\Gamma }_s$ and $\Delta {\Gamma }_s$ cannot benefit from the excellent time resolution and tagging power of the future $Z$-factories. Only operating at 10-Tera-$Z$ mode can the ${\Gamma }_s$ and $\Delta {\Gamma }_s$ reach an 18\% larger precision than the precision expected to be obtained from LHCb at HL-LHC. The control of penguin contamination at the future Z-factories is also discussed.

Comments: Updated with the version accepted by EPJC