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

Abstract

We formulate the most-general time-dependent decay distributions of $B_s\to J/\psi (\to l^{+}{l}^{-})\varphi (\to K^{+}{K}^{-})$ in which the direct CP violation is explicitly incorporated. We then 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 various QCD corrections and the hard-spectator diagrams. With the inclusion of these sizable corrections, our theoretical results for CP-averaged branching ratios, polarization fractions, CP-violating asymmetries, and relative phases are in good consistency 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 $\mathcal{O}(10^{-3})$.

19 pages, 3 figures; v2: ratios of branching fractions updated

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