We formulate the most general time-dependent distributions of $B_s\to J/\psi (\to l^{+}{l}^{-})\varphi (\to K^{+}{K}^{-})$ in which the direct charge parity ($CP$) violation is explicitly incorporated. We investigate the $B\to J/\psi V$ decays in the perturbative QCD approach where $V$ is a light vector meson. Apart from the leading-order factorizable contributions, we also take into account QCD vertex corrections and the hard-spectator diagrams. With the inclusion of these sizable corrections, most of our theoretical results for $CP$-averaged branching ratios, polarization fractions, $CP$-violating asymmetries, and relative phases are consistent with the available data. Based on the global agreement, we further explore the penguin contributions and point out that the ${\varphi }_s$ extracted from $B_s\to J/\psi \varphi$ can be shifted away by $\mathcal{O}({10}^{-3})$.

• Received 5 September 2013

DOI:https://doi.org/10.1103/PhysRevD.89.094010