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We formulate the most-general time-dependent decay distributions of $B_s\toJ/\psi (\to l^+l^-) \phi(\to K^+K^-)$ in which the direct CP violation isexplicitly incorporated. We then investigate the $B \to J/\psi V$ decays in theperturbative QCD approach where $V$ is a light vector meson. Apart from theleading-order factorizable contributions, we also take into account various QCDcorrections and the hard-spectator diagrams. With the inclusion of thesesizable corrections, our theoretical results for CP-averaged branching ratios,polarization fractions, CP-violating asymmetries, and relative phases are ingood consistency with the available data. Based on the global agreement, wefurther explore the penguin contributions and point out that the $\phi_s$extracted from $B_s\to J/\psi \phi$ can be shifted away by ${\cal O}(10^{-3})$.

Penguin Pollution in $B\to J/\psi V$ Decays and Impact on the Extraction of the $B_s-\bar B_s$ mixing phase