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

TL;DR

This paper develops a comprehensive framework for analyzing $B_s o J/ \, ext{V}$ decays, incorporating QCD corrections and penguin contributions, which impacts the precision extraction of the $B_s-ar{B}_s$ mixing phase.

Contribution

It provides the most-general time-dependent decay distribution including direct CP violation and assesses penguin effects on the mixing phase extraction.

Findings

Theoretical predictions agree with experimental data for branching ratios and CP asymmetries.

QCD corrections significantly affect polarization and CP-violating observables.

Penguin contributions can shift the mixing phase by approximately 10^{-3}.

Abstract

We formulate the most-general time-dependent decay distributions of $B_s\to J/\psi (\to l^+l^-) \phi(\to K^+K^-)$ 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 $\phi_s$ extracted from $B_s\to J/\psi \phi$ can be shifted away by ${\cal O}(10^{-3})$.