Generalized Study with Isospin-phased Topological Approach on the $B \to Kπ$ Puzzle
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We study the decay processes $B \to K π$ by using generalized decay amplitudes with both the final state re-scattering strong phases and the topological quark diagrammatic strong phases included together as part of fitting parameters. Using a generalized approach, so called ``isospin phased topological approach'', for all the currently available data of $B \to K π$ decays, we determine the allowed values of the relevant theoretical parameters, corresponding to the electroweak penguin, the color-suppressed tree contribution, strong phase differences, etc. In order to find the most likely values of the parameters in a statistically reliable way, we use the $χ^2$ minimization technique. We find that the long distance final state re-scattering, when taken at proper value, can provide a reasonable fit to the standard model with the perturbative QCD estimated values, and therefore, it is premature to conclude that it requires new physics to explain the CP violating $B \to Kπ$ data.
21 pages, 4 tables Talk given at the third International Conference on Flavor Physics (ICFP 2005), National Central University, Chong-li, Taiwan, R.O.C, 3-8 Oct 2005. A table added. Comments and References added. Notation of formulas modified
21 pages, 4 tables Talk given at the third International Conference on Flavor Physics (ICFP 2005), National Central University, Chong-li, Taiwan, R.O.C, 3-8 Oct 2005. A table added. Comments and References added. Notation of formulas modified