Controlling Rescattering Effects in Constraints on the CKM Angle $\gamma$ arising from $B\to \pi K$ Decays

Abstract

It has recently been pointed out that the observables of the decay $B^{+}\to K^{+}\overline{K^0}$ and its charge conjugate allow us to take into account rescattering effects in constraints on the CKM angle $\gamma$ arising from $B^{\pm }\to {\pi }^{\pm }K$ and $B_d\to {\pi }^{\pm }{K}^{\pm }$ modes, and that they play an important role to obtain insights into final-state interactions. In this paper, the formalism needed to accomplish this task is discussed in detail. Furthermore, using a transparent model to describe the rescattering processes, as well as electroweak penguins, we calculate the quantities parametrizing the $B^{+}\to {\pi }^{+}{K}^0$ and $B_d^0\to {\pi }^{-}{K}^{+}$ decay amplitudes for specific examples, and illustrate the constraints on $\gamma$ arising from the corresponding observables. Although this model is very crude, it shows nicely the power of $B^{\pm }\to K^{\pm }K$ both to include the rescattering effects in the bounds on $\gamma$ and to obtain insights into final-state interactions. Moreover this model exhibits the interesting feature that the combined branching ratio BR$(B^{\pm }\to K^{\pm }K)$ may be considerably enhanced through rescattering processes, as was recently pointed out within a general framework.

14 pages, LaTeX, 4 figures

References in corpus (3)

• Final State Interactions and New Physics in B -> pi K Decays
• Observation of Exclusive Two-Body B Decays to Kaons and Pions
• Final State Interaction Phases in $B\to K\pi$ Decay Amplitudes

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