We study the impacts of the nonuniversal $Z^{\prime }$ model, providing flavor-changing neutral current at tree level, on the branching ratios (BRs), CP asymmetries (CPAs), and polarization fractions of $B$ decays. We find that, for satisfying the current data, the new left- and right-handed couplings have to be included at the same time. The new introduced effective interactions not only could effectively explain the puzzle of small longitudinal polarization in $B\to K^{*}\varphi$ decays, but also provide a solution to the small CPA of $B^{\pm }\to {\pi }^0{K}^{\pm }$. We also find that the favorable CPA of $B^{\pm }\to {\pi }^0{K}^{\pm }$ is opposite in sign to the standard model; meanwhile, the CPA of $B_d\to {\pi }^{0}K$ has to be smaller than $-10\%$. In addition, by using the values of parameters which are constrained by $B\to \pi K$, we find that the favorable ranges of BRs, CPAs, longitudinal polarizations, and perpendicular transverse polarizations for $(B^{\pm }\to {\rho }^{\pm }{K}^{*},B_d\to {\rho }^{\mp }{K}^{*\pm })$ are $(17.1\pm 3.9,10.0\pm 2.0)\times {10}^{-6}$, $(3\pm 5,21\pm 7)\%$, $(0.66\pm 0.10,0.44\pm 0.08)$, and $(0.14\pm 0.10,0.25\pm 0.09)$, respectively.

• Received 16 January 2006

DOI:https://doi.org/10.1103/PhysRevD.73.075003