CP phase of nonuniversal $Z^{\prime }$ on $\sin {\varphi }_s^{J/\Psi \varphi }$ and T-odd observables of ${\bar{B}}_q\to V_q{\ell }^{+}{\ell }^{-}$

Abstract

The evidence of a large CP phase has been shown by CDF and DØ collaborations in the time-dependent CP asymmetry (CPA) of $B_s\to J/\Psi \varphi$ decay, where the nonvanished CPA clearly implies the existence of a non-Kobayashi-Maskawa phase in $b\to s$ transition. We study the new phases originated by the extra family dependent $U(1{)}^{\prime }$ model and examine their impact on $\hat{T}$ or CP violating observables in ${\bar{B}}_q\to V_q{\ell }^{+}{\ell }^{-}$ decays with $V_q=K^{\ast }(\varphi )$. Adopting the constraints from the current data of $\Delta m_s$ and the branching ratios for ${\bar{B}}_s\to {\mu }^{+}{\mu }^{-}$ and ${\bar{B}}_q\to V_q{\ell }^{+}{\ell }^{-}$, we find that ${\varphi }_s^{J/\Psi \varphi }=-(0.26\pm 0.22)$ and the T-odd observables of above 10% in the decay chain ${\bar{B}}_q\to V_q(\to K\pi [KK]){\ell }^{+}{\ell }^{-}$ can be achieved. In addition, we demonstrate that the longitudinal and transverse polarizations of $K^{\ast }$ and the up-down asymmetry of $K$ in the same decay chain are also sensitive to the $Z^{\prime }$-mediated effects.

Comments: 13 pages, 3 figures, references added, final version to appear in PLB