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

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

1997-11-07

arxiv.org/abs/hep-ph/9711262v3

Nucl.Phys. B533 (1998) 3-24

Physics

High Energy Physics

High Energy Physics - Phenomenology

Some mistakes in the equations have been corrected, conclusions have been changed slightly. The complete paper, including figu

Scientific paper

10.1016/S0550-3213(98)00506-9

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 $B^+\to\{\pi^0K^+\}\to\pi^+K^0$. 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.

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