We report a measurement of the bottom-strange meson mixing phase ${\beta }_s$ using the time evolution of $B_s^0\to J/\psi (\to {\mu }^{+}{\mu }^{-})\varphi (\to K^{+}{K}^{-})$ decays in which the quark-flavor content of the bottom-strange meson is identified at production. This measurement uses the full data set of proton-antiproton collisions at $\sqrt{s}=1.96\mathrm{TeV}$ collected by the Collider Detector experiment at the Fermilab Tevatron, corresponding to $9.6{\mathrm{fb}}^{-1}$ of integrated luminosity. We report confidence regions in the two-dimensional space of ${\beta }_s$ and the $B_s^0$ decay-width difference $\Delta {\Gamma }_s$ and measure ${\beta }_s\in [-\pi /2,-1.51]\cup [-0.06,0.30]\cup [1.26,\pi /2]$ at the 68% confidence level, in agreement with the standard model expectation. Assuming the standard model value of ${\beta }_s$, we also determine $\Delta {\Gamma }_s=0.068\pm 0.026(\mathrm{stat})\pm 0.009(\mathrm{syst}){\mathrm{ps}}^{-1}$ and the mean $B_s^0$ lifetime ${\tau }_s=1.528\pm 0.019(\mathrm{stat})\pm 0.009(\mathrm{syst})\mathrm{ps}$, which are consistent and competitive with determinations by other experiments.

• Received 14 August 2012

DOI:https://doi.org/10.1103/PhysRevLett.109.171802