A Comprehensive Analysis of Hadronic b->s Transitions in a Family Non-universal Z' Model

Abstract

Motivated by the latest improved measurements of B-meson decays, we make a comprehensive analysis of the impact of a family non-universal $Z^{\prime }$ boson on $B_s-{\bar{B}}_s$ mixing and two-body hadronic B-meson decays, all being characterized by the quark-level $b\to s$ transition. Explicitly 22 decay modes and the related 52 observables are considered, and some interesting correlations between them are also carefully examined. Firstly, the allowed oases of $b-s-Z^{\prime }$ coupling parameters $|B_{sb}^{L,R}|$ and ${\varphi }_s^{L,R}$ are extracted from $B_s-{\bar{B}}_s$ mixing. Then, in the "SM limit"~({\it i.e.,} no new types of $Z^{\prime }$-induced four-quark operators arise compared to the SM case), we study the $Z^{\prime }$ effects on $B\to \pi K$, $\pi K^{\ast }$ and $\rho K$ decays. It is found that a new weak phase ${\varphi }_s^L\sim -90^{\circ }$ is crucial for resolving the observed "$\pi K$ CP puzzle" and the allowed oases of the other $Z^{\prime }$ coupling parameters are also strongly restricted. Moreover, the $Z^{\prime }$ effects on ${\bar{B}}_s\to KK$, $K{K}^{\ast }$ and ${\pi }^0\varphi$ decays, being induced by the same quark-level $b\to sq\bar{q}(q=u,d)$ transitions, are also investigated. Especially, it is found that the decay ${\bar{B}}_s\to {\pi }^0\varphi$, once measured, would play a key role in revealing the observed "$\pi K$ CP puzzle" and probing possible new physics hints. Finally, to check the non-universality of $Z^{\prime }$ couplings to light-quark pairs, we have studied the $B\to \varphi K$ decays in detail and found that the left-handed $s-s-Z^{\prime }$ coupling is different from the $d-d-Z^{\prime }$ one, which is due to the large $A_{CP}^{dir}(B^{-}\to \varphi K^{-})$ reported by the BaBar collaboration.

Comments: 38 pages, 11 figures; To appear in JPG