Rescattering and Electroweak Penguin Effects in Strategies to Constrain and Determine the CKM Angle $\gamma$ from $B\to \pi K$ Decays

Abstract

A general parametrization of the $B^{+}\to {\pi }^{+}{K}^0$ and $B_d^0\to {\pi }^{-}{K}^{+}$ decay amplitudes is presented. It relies only on the isospin symmetry of strong interactions and the phase structure of the Standard Model and involves no approximations. In particular, this parametrization takes into account both rescattering and electroweak penguin effects, which limit the theoretical accuracy of bounds on $\gamma$ arising from the combined $B^{\pm }\to {\pi }^{\pm }K$, $B_d\to {\pi }^{\mp }{K}^{\pm }$ branching ratios. Generalized bounds making also use of the CP asymmetry in the latter decay are derived, and their sensitivity to possible rescattering and electroweak penguin effects is investigated. It is pointed out that experimental data on $B^{\pm }\to K^{\pm }K$ allow us to include rescattering processes in these bounds completely, and an improved theoretical treatment of electroweak penguins is presented. It is argued that rescattering effects may enhance the combined $B^{\pm }\to K^{\pm }K$ branching ratio by a factor of $\mathcal{O}(10)$ to the $10^{-5}$ level, and that they may be responsible for the small present central value of the ratio of the combined $B_d\to {\pi }^{\mp }{K}^{\pm }$ and $B^{\pm }\to {\pi }^{\pm }K$ branching ratios, which has recently been reported by the CLEO collaboration and, if confirmed, would exclude values of $\gamma$ within a large region around $90^{\circ }$.

42 pages, LaTeX, 20 figures

Cited by in corpus (9)

• Two body B decays with isosinglet final states in SCET
• The B -> pi K Puzzle and its Relation to Rare B and K Decays
• Effective Lifetimes of $B_s$ Decays and their Constraints on the $B_s^0$-${\bar{B}}_s^0$ Mixing Parameters
• Anatomy of $B_{s,d}^0\to J/\psi f_0(980)$
• $B_{s,d}\to \pi \pi ,\pi K,KK$: Status and Prospects
• Large electroweak penguin contribution in B -> K pi and pi pi decay modes
• New Aspects of B -> pi pi, pi K and their Implications for Rare Decays
• Polarization, CP Asymmetry and Branching ratios in B \to K^* K^* with Perturbative QCD approach
• Evidence for B+ -> K0barK+ and B0 -> K0K0bar, and Measurement of the Branching Fraction and Search for Direct CP Violation in B+ -> K0pi+