Penguin Topologies, Rescattering Effects and Penguin Hunting with $B_{u,d}\to K\bar{K}$ and $B^{\pm }\to {\pi }^{\pm }K$

Abstract

In the recent literature, constraints on the CKM angle $\gamma$ arising from the branching ratios for $B^{\pm }\to {\pi }^{\pm }K$ and $B_d\to {\pi }^{\mp }{K}^{\pm }$ decays received a lot of attention. An important theoretical limitation of the accuracy of these bounds is due to rescattering effects, such as $B^{+}\to \{{\pi }^0{K}^{+}\}\to {\pi }^{+}{K}^0$. We point out that these processes are related to penguin topologies with internal up quark exchanges and derive SU(2) isospin relations among the $B^{+}\to {\pi }^{+}{K}^0$ and $B_d^0\to {\pi }^{-}{K}^{+}$ decay amplitudes by defining ``tree'' and ``penguin'' amplitudes in a proper way, allowing the derivation of generalized bounds on the CKM angle $\gamma$. We propose strategies to obtain insights into the dynamics of penguin processes with the help of the decays $B_{u,d}\to K\bar{K}$ and $B^{\pm }\to {\pi }^{\pm }K$, derive a relation among the direct CP-violating asymmetries arising in these modes, and emphasize that rescattering effects can be included in the generalized bounds on $\gamma$ completely this way. Moreover, we have a brief look at the impact of new physics.

Some mistakes in the equations have been corrected, conclusions have been changed slightly. The complete paper, including figures, is also available via anonymous ftp at ftp://ttpux2.physik.uni-karlsruhe.de/, or via www at http://www-ttp.physik.uni-karlsruhe.de/cgi-bin/preprints/

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