Prospect for measurement of the CP-violating phase  $$\phi _s$$ ϕ s in the $$B_{s}\rightarrow J/\psi \phi $$ B s → J / ψ ϕ channel at a future Z factory

Abstract

Abstract The CP-violating phase $$\phi _s$$ ϕ s , the $$B_{s}$$ B s decay width ( $$\varGamma _s$$ Γ s ), and the $$B_{s}$$ B s decay width difference ( $$\varDelta \varGamma _s$$ Δ Γ 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: $$\sigma (\phi _s) = 4.6~\textrm{mrad}$$ σ ( ϕ s ) = 4.6 mrad , $$\sigma (\varDelta \varGamma _s) = 2.4~\mathrm {ns^{-1}}$$ σ ( Δ Γ s ) = 2.4 ns - 1 and $$\sigma (\varGamma _s) = 0.72~\mathrm {ns^{-1}}$$ σ ( Γ s ) = 0.72 ns - 1 . The precision of $$\phi _s $$ 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 $$\phi _s $$ ϕ s can be measured at 45% of the precision obtained from the LHCb experiment at HL-LHC. However, the measurement of $$\varGamma _s$$ Γ s and $$\varDelta \varGamma _s$$ Δ Γ 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 $$\varGamma _s$$ Γ s and $$\varDelta \varGamma _s$$ Δ Γ 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.