First Flavor-Tagged Determination of Bounds on Mixing-Induced $\textit{CP}$ Violation in $B_s^0 \rightarrow J/\psi\,\phi$ Decays

We describe the first determination of bounds on the $\textit{CP}$-violation parameter $2\beta_s$ using $B_s^0$ decays in which the flavor of the bottom meson at production is identified. The result is based on $B_s^0 \rightarrow J/\psi\,\phi$ decays collected with the CDF\,II detector using $p\bar p$~collisions produced at the Fermilab Tevatron. We report confidence regions in the two-dimensional space of $2\beta_s$ and the decay-width difference $\Delta\Gamma$ and present the latest results.