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

Abstract

In the recent literature, constraints on the CKM angle $γ$ arising from the branching ratios for $B^\pm\toπ^\pm K$ and $B_d\toπ^\mp K^\pm$ decays received a lot of attention. An important theoretical limitation of the accuracy of these bounds is due to rescattering effects, such as $B^+\to\{π^0K^+\}\toπ^+K^0$. We point out that these processes are related to penguin topologies with internal up quark exchanges and derive SU(2) isospin relations among the $B^+\toπ^+K^0$ and $B_d^0\toπ^-K^+$ decay amplitudes by defining ``tree'' and ``penguin'' amplitudes in a proper way, allowing the derivation of generalized bounds on the CKM angle $γ$. 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 $B^\pm\toπ^\pm K$, 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 $γ$ completely this way. Moreover, we have a brief look at the impact of new physics.