Revisiting B\to\pi K, \pi K^{\ast} and \rho K decays: CP violations and implication for New Physics

TL;DR

This paper analyzes B to pi K, pi K*, and rho K decays using QCD factorization, finding that annihilation amplitudes and potential new physics contributions could explain observed CP violation patterns and resolve existing puzzles.

Contribution

It introduces a model-independent analysis of new physics operators affecting B decays, incorporating an infrared finite gluon propagator and exploring their impact on CP violations.

Findings

Branching ratios and CP violations mostly agree with data using an effective gluon mass.

Both annihilation strong phases and new weak phases may be needed to explain the pi K puzzle.

Good agreement with experimental data on mixing-induced CP violations supports the new physics hypothesis.

Abstract

Combining the up-to-date experimental information on $B\to\pi K, \pi K^{\ast}$ and $\rho K$ decays, we revisit the decay rates and CP asymmetries of these decays within the framework of QCD factorization. Using an infrared finite gluon propagator of Cornwall prescription, we find that the time-like annihilation amplitude could contribute a large strong phase, while the space-like hard spectator scattering amplitude is real. Numerically, we find that all the branching ratios and most of the direct CP violations, except $A_{CP}(B^{\pm}\to K^{\pm}\pi^{0})$, agree with the current experimental data with an effective gluon mass $m_g\simeq0.5 {\rm GeV}$. Taking the unmatched difference in direct CP violations between $B\to\pi^{0} K^{\pm}$ and $\pi^{\mp}K^{\pm}$ decays as a hint of new physics, we perform a model-independent analysis of new physics contributions with a set of $\bar{s}(1+\gamma_{5})b\otimes\bar{q}(1+\gamma_{5})q$ (q=u,d) operators. Detail analyses of the relative impacts of the operators are presented in five cases. Fitting the twelve decay modes, parameter spaces are found generally with nontrivial weak phases. Our results may indicate that both strong phase from annihilation amplitude and new weak phase from new physics are needed to resolve the $\pi K$ puzzle. To further test the new physics hypothesis, the mixing-induced CP violations in $B\to\pi^{0}K_{S}$ and $\rho^{0}K_{S}$ are discussed and good agreements with the recent experimental data are found.