The Effects of a Family Non-universal Z' Boson in the \bar{B}_s->\pi K, \pi K*, \rho K Decays and B_d-\bar{B_d} mixing

Abstract

We revisit ${\bar{B}}_s\to \pi K$, $\pi K^{\ast }$ and $\rho K$ decays within QCDF formalism and examine the possible effects of a family non-universal $Z^{\prime }$ boson in these decays. In our evaluations, the strong constraints from $B_d-\overline{B_d}$ mixing on the strength of the left-handed flavor-changing $d-b-Z^{\prime }$ coupling $B_{db}^L$ ~($\sim 0.2\times 10^{-3}$) is also included. Numerically, we find that a new weak phase ${\varphi }_d^L\sim -50^{\circ }$ involved in $B_{db}^L$, the negative combination of the $u-u-Z^{\prime }$ and $d-d-Z^{\prime }$ couplings $P_{ud}^R$ and/or $D_{ud}^L$ with larger absolute value are crucial to improve the agreement of $\mathcal{B}({\bar{B}}_s\to {\pi }^{-}{K}^{+})$ between the SM prediction and the experimental measurement. Generally, $\mathcal{B}({\bar{B}}_s\to {\pi }^{-}{K}^{+})$ could be reduced by about 18% at most by $Z^{\prime }$ contributions. Moreover, combining with the recent updated measurement on ${\beta }_s$ by CDF and D0 collaborations, we also find that $Z^{\prime }$ effects in ${\bar{B}}_s\to {\pi }^{-}{K}^{+}$ decays are very important for examining whether the CKM-like hierarchy persists in a family non-universal $Z^{\prime }$ coupling matrix.

Comments: 20 pages, 4 figures; final version to appear in Nucl. Phys. B