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 $γ$ 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$(B^+\toπ^0K^+)$, BR$(B^-\toπ^0K^-)$, BR$(B^+\toπ^+K^0)$ and ii) either BR$(B^0_d\toπ^-K^+)$, BR$(\bar B^0_d\toπ^+K^-)$ or $\acp(t)$ of the mode $B_s\to K^+K^-$. The determination employing the $B\toπK$ 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 $α$ by using isospin relations among $B\toππ$ decays. Our results allow in principle the determination of CKM-phases in a variety of $B$-decays.