Constraints on the nonuniversal Z′ couplings from B → πK, πK* and ρK Decays

Motivated by the large difference between the direct CP asymmetries A(CP)(B- -> pi K-0(-)) and A(CP) ((B) over bar (0) -> pi K-+(-)), we combine the up-to-date experimental information on B -> pi K, pi K* and rho K decays to pursue possible solutions with the nonuniversal Z' model. Detailed analyses of the relative impacts of different types of couplings are presented in four specific cases. Numerically, we find that the new coupling parameters, xi(LL) and xi(LR) with a common nontrivial new weak phase phi(L) similar to -86 degrees, which are relevant to the Z' contributions to the electroweak penguin sector Delta C-9 and Delta C-7, are crucial to the observed "pi K puzzle". Furthermore, they are found to be definitely unequal and opposite in sign. We also find that A(CP)(B- -> rho(0) K-) can put a strong constraint on the new Z' couplings, which implies the Z' contributions to the coefficient of QCD penguins operator O-3 involving the parameter zeta(LL) required.