Strategies for Fixing the CKM-angle $\gamma$ and Obtaining Experimental Insights into the World of Electroweak Penguins

Abstract

Using the $SU(3)$ flavour symmetry of strong interactions, we propose strategies for extracting both the CKM-angle $\gamma$ and the $\bar{b}\to \bar{u}u\bar{s}$ tree-level amplitude $T^{\prime }$. We present also an approximate approach using the branching ratios for the modes $B^{+}\to {\pi }^{+}{K}^0$, $B_d^0\to {\pi }^{-}{K}^{+}$, ${\bar{B}}_d^0\to {\pi }^{+}{K}^{-}$ and $B^{+}\to {\pi }^{+}{\pi }^0$ which should be rather promising from the experimental point of view. The quantities $\gamma$ and $T^{\prime }$ determined this way may well be used as an input to control electroweak penguins in nonleptonic $B$-decays as has been discussed in previous work. Following these lines, we propose strategies for obtaining quantitative insights into the physics of the electroweak penguin operators and performing some consistency checks. As a by-product, we derive an upper bound of $6^{\circ }$ for the uncertainty originating from electroweak penguins in the $\alpha$-determination by means of $B\to \pi \pi$ decays.

Comments: 15 pages, LaTeX, Figures not included