Measurement of CP violation in Bs--> J/psi Phi decays using the full CDF data set

We report on the final measurement of the \CP-violating \Bs\ mixing phase \betas\ in $\sqrt{s}=$1.96 TeV proton-antiproton collisions collected with the Collider Detector at the Fermilab Tevatron collider. Using a sample corresponding to 9.6\,\lumifb\ of integrated luminosity, we fit the decay-time evolution of $B^0_s \rightarrow J/\psi (\rightarrow \mu^+ \mu^-) \phi (\rightarrow K^+ K^-)$ decays in which the $b$-quark content at production and the \CP\ parity of the final state are identified. The interference of decays with and without mixing renders the \Bs\ mixing phase observable. The phase is determined to be $-0.06<\betas <0.30$ at 68\% confidence level. The decay-width difference between heavy and light \Bs\ eigenstates, and the average \Bs\ lifetime are also determined to be \DGs $= 0.068 \pm 0.027$ $\rm{ps^{-1}}$ and $\tau_s\,=1.528 \pm 0.021$ $\rm{ps}$, respectively. These results are among the world's most precise from a single experiment, and compatible with standard model predictions.