Measurement of the Bottom-Strange Meson Mixing Phase in the Full CDF Data Set

We report a measurement of the bottom-strange meson mixing phase βₛ using the time evolution of ${B}ₛ⁰{→}J/{ψ}({→}{{μ}}⁺{{μ}}^{{-}}){φ}({→}{K}⁺{K}^{{-}})$ 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 $√s=1.96 TeV$ collected by the Collider Detector experiment at the Fermilab Tevatron, corresponding to $9.6 {fb}^{{-}1}$ of integrated luminosity. We report confidence regions in the two-dimensional space of ${{β}}ₛ$ and the ${B}ₛ⁰$ decay-width difference ${Δ}{{Γ}}ₛ$ and measure ${{β}}ₛ{∈}[{-}{π}/2,{-}1.51]{∪}[{-}0.06,0.30]{∪}[1.26,{π}/2]$ at the 68% confidence level, in agreement with the standard model expectation. Assuming the standard model value of ${{β}}ₛ$, we also determine ${Δ}{{Γ}}ₛ=0.068±{}0.026(stat)±{}0.009(syst) {ps}^{{-}1}$ and the mean ${B}ₛ⁰$ lifetime ${{τ}}ₛ=1.528±{}0.019(stat)±{}0.009(syst) ps$, which are consistent and competitive with determinations by other experiments.