The effects of a family non-universal Z-prime boson on B--->pipi decays

Motivated by the measured large branching ratio of $\bar{B}^{0}\to\pi^0\pi^0$ (the so-called "$\pi\pi$" puzzle), we investigate the effects of a family non-universal $Z^{\prime}$ model on the tree-dominated $B\to\pi\pi$ decays. We find that the $Z^{\prime}$ coupling parameter $\zeta_{d}^{LR}\sim0.05$ with a nontrivial new weak phase $\phi_d^L\sim-50^{\circ}$, which is relevant to the $Z^{\prime}$ contributions to the QCD penguin sector $\triangle C_5$, is needed to reconcile the observed discrepancy. Combined with the recent fitting results from $B\to\pi K$, $\pi K^{\ast}$ and $\rho K$ decays, the $Z^{\prime}$ parameter spaces are severely reduced but still not excluded entirely, implying that both the "$\pi\pi$" and "$\pi K$" puzzles could be accommodated simultaneously within such a family non-universal $Z^{\prime}$ model.