First Flavor-Tagged Determination of Bounds on Mixing-Induced<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>C</mml:mi><mml:mi>P</mml:mi></mml:math>Violation in<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:msubsup><mml:mi>B</mml:mi><mml:mi>s</mml:mi><mml:mn>0</mml:mn></mml:msubsup><mml:mo>→</mml:mo><mml:mi>J</mml:mi><mml:mo>/</mml:mo><mml:mi>ψ</mml:mi><mml:mi>ϕ</mml:mi></mml:math>Decays

This Letter describes the first determination of bounds on the $CP$-violation parameter $2{\ensuremath{\beta}}_{s}$ using ${B}_{s}^{0}$ decays in which the flavor of the bottom meson at production is identified. The result is based on approximately 2000 ${B}_{s}^{0}\ensuremath{\rightarrow}J/\ensuremath{\psi}\ensuremath{\phi}$ decays reconstructed in a $1.35\text{ }\text{ }{\mathrm{fb}}^{\ensuremath{-}1}$ data sample collected with the CDF II detector using $p\overline{p}$ collisions produced at the Fermilab Tevatron. We report confidence regions in the two-dimensional space of $2{\ensuremath{\beta}}_{s}$ and the decay-width difference $\ensuremath{\Delta}\ensuremath{\Gamma}$. Assuming the standard model predictions of $2{\ensuremath{\beta}}_{s}$ and $\ensuremath{\Delta}\ensuremath{\Gamma}$, the probability of a deviation as large as the level of the observed data is 15%, corresponding to 1.5 Gaussian standard deviations.

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