Prospect for measurement of the CP-violating phase $ϕ_s$ in the $B_{s}\rightarrow J/ψϕ$ channel at a future Z factory

Abstract

The CP-violating phase $ϕ_s$, the \Bs decay width ($Γ_s$), and the \Bs decay width difference ($ΔΓ_s$) 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: $σ(ϕ_s) = 4.6~\mathrm{mrad}$, $σ(ΔΓ_s) = 2.4~\mathrm{ns^{-1}}$ and $σ(Γ_s) = 0.72~\mathrm{ns^{-1}}$. The precision of $ϕ_s$ is 40\% larger than the expected precision with the LHCb experiment at HL-LHC. If operating at 10-Tera-$Z$ mode, the precision of $ϕ_s$ can be measured at 45\% of the precision obtained from the LHCb experiment at HL-LHC. However, the measurement of $Γ_s$ and $ΔΓ_s$ cannot benefit from the excellent time resolution and tagging power of the future $Z$-factories. Only operating at 10-Tera-$Z$ mode can the $Γ_s$ and $ΔΓ_s$ 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.