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

Abstract

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 ${\zeta }_d^{LR}\sim 0.05$ with a nontrivial new weak phase ${\varphi }_d^L\sim -50^{\circ }$, which is relevant to the $Z^{\prime }$ contributions to the QCD penguin sector $△C_5$, 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.

Comments: 28 pages, 4 figures. References and discussions added. To appear in IJMPA