We present a measurement of the $CP$-violating parameter ${\beta }_s^{J/\psi \varphi }$ using approximately 6500 $B_s^0\to J/\psi \varphi$ decays reconstructed with the CDF II detector in a sample of $p\overline{p}$ collisions at $\sqrt{s}=1.96\mathrm{TeV}$ corresponding to $5.2{\mathrm{fb}}^{-1}$ integrated luminosity produced by the Tevatron collider at Fermilab. We find the $CP$-violating phase to be within the range ${\beta }_s^{J/\psi \varphi }\in [0.02,0.52]\cup [1.08,1.55]$ at 68% confidence level where the coverage property of the quoted interval is guaranteed using a frequentist statistical analysis. This result is in agreement with the standard model expectation at the level of about one Gaussian standard deviation. We consider the inclusion of a potential $S$-wave contribution to the $B_s^0\to J/\psi K^{+}{K}^{-}$ final state which is found to be negligible over the mass interval $1.009<m(K^{+}{K}^{-})<1.028\mathrm{GeV}/c^2$. Assuming the standard model prediction for the $CP$-violating phase ${\beta }_s^{J/\psi \varphi }$, we find the $B_s^0$ decay width difference to be $\Delta {\Gamma }_s=0.075\pm 0.035(\mathrm{stat})\pm 0.006(\mathrm{syst}){\mathrm{ps}}^{-1}$. We also present the most precise measurements of the $B_s^0$ mean lifetime $\tau (B_s^0)=1.529\pm 0.025(\mathrm{stat})\pm 0.012(\mathrm{syst})\mathrm{ps}$, the polarization fractions $|A_0(0){|}^2=0.524\pm 0.013(\mathrm{stat})\pm 0.015(\mathrm{syst})$ and $|A_{\parallel }(0){|}^2=0.231\pm 0.014(\mathrm{stat})\pm 0.015(\mathrm{syst})$, as well as the strong phase ${\delta }_{\perp }=2.95\pm 0.64(\mathrm{stat})\pm 0.07(\mathrm{syst})\mathrm{rad}$. In addition, we report an alternative Bayesian analysis that gives results consistent with the frequentist approach.

• Received 7 December 2011

DOI:https://doi.org/10.1103/PhysRevD.85.072002