Nonuniversal $Z^{\prime}$ couplings in B decays

We study the impacts of 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 $B\to K^* \phi$ 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 $(17.1\pm 3.9, 10.0\pm2.0)\times 10^{-6}$, $(3\pm 5, 21\pm 7)$, $(0.66\pm 0.10, 0.44\pm 0.08)$ and $(0.14\pm 0.10, 0.25\pm 0.09)$, respectively.