Constraints on the nonuniversal Z^\prime couplings from B\to\pi K, \pi K^{\ast} and \rho K Decays

Abstract

Motivated by the large difference between the direct CP asymmetries $A_{CP}(B^{-}\to {\pi }^0{K}^{-})$ and $A_{CP}({\bar{B}}^0\to {\pi }^{+}{K}^{-})$, we combine the up-to-date experimental information on $B\to \pi K$, $\pi K^{\ast }$ and $\rho K$ decays to pursue possible solutions with the nonuniversal $Z^{\prime }$ 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 ${\varphi }_L\sim -86^{\circ }$, which are relevant to the $Z^{\prime }$ contributions to the electroweak penguin sector $△C_9$ and $△C_7$, are crucial to the observed "$\pi K$ puzzle". Furthermore, they are found to be definitely unequal and opposite in sign. We also find that $A_{CP}(B^{-}\to {\rho }^0{K}^{-})$ can put a strong constraint on the new $Z^{\prime }$ couplings, which implies the $Z^{\prime }$ contributions to the coefficient of QCD penguins operator $O_3$ involving the parameter ${\zeta }^{LL}$ required.

Comments: 27 pages, 6 figures. References and a note added