Towards the Control over Electroweak Penguins in Nonleptonic B-Decays

Abstract

We present strategies for determining electroweak penguins from experimental data. Using the CKM-angle $\gamma$ as one of our central inputs and making some reasonable approximations, we show that the $\bar{b}\to \bar{s}$ electroweak penguin amplitude can be determined in a two-step procedure involving i) BR$(B^{+}\to {\pi }^0{K}^{+})$, BR$(B^{-}\to {\pi }^0{K}^{-})$, BR$(B^{+}\to {\pi }^{+}{K}^0)$ and ii) either BR$(B_d^0\to {\pi }^{-}{K}^{+})$, BR$({\bar{B}}_d^0\to {\pi }^{+}{K}^{-})$ or $\text{acp}(t)$ of the mode $B_s\to K^{+}{K}^{-}$. The determination employing the $B\to \pi K$ transitions is not affected by $SU(3)$-breaking effects. Relating the $\bar{b}\to \bar{s}$ electroweak penguin amplitude to the $\bar{b}\to \bar{d}$ case through $SU(3)$ symmetry arguments, we are in a position to estimate the electroweak penguin uncertainty affecting the extraction of the CKM-angle $\alpha$ by using isospin relations among $B\to \pi \pi$ decays. Our results allow in principle the determination of CKM-phases in a variety of $B$-decays.

Comments: 14 pages, LaTeX, Figures not included