5 v 2 1 1 O ct 2 00 4 Weak phases from the B → ππ , Kπ decays

Recent data of two-body nonleptonic B meson decays allow a topological-amplitude analysis up to the O(λ2) accuracy, where λ denotes the Wolfenstein parameter. We find an exact solution from the B → ππ data and an exact solution from the B → Kπ data, which satisfy the approximate SU(3) flavor symmetry. These solutions indicate that the color-suppressed tree amplitude is large, all other amplitudes can be understood within the standard model, and the weak phases φ2 ≈ 90 and φ3 ≈ 60 are consistent with the global unitarity triangle fit. Email: [email protected] Email: [email protected] To determine the weak phases in the Kobayashi-Maskawa ansatz for CP violation [1], one either resorts to theoretically clean modes, which are usually experimentally difficult, or to the modes with higher feasibility, which, however, require theoretical inputs [2]. Recently, we have adopted the topological-amplitude parametrization for two-body nonleptonic B meson decays, in which the theoretical inputs are the counting rules for various decay amplitudes [3] in terms of powers of the Wolfenstein parameter λ ∼ 0.22. These counting rules are supported by the known QCD theories [4, 5, 6, 7], and slightly different from those postulated in [8]. The strategy of this method is to drop the topologies with higher powers of λ until the number of free parameters are equal to the number of available measurements. The weak phases and the amplitudes are then solved exactly by comparing the resultant parametrization with experimental data. Afterwards, it should be examined whether the obtained amplitudes obey the power counting rules. If they do, the extracted weak phases suffer only the theoretical uncertainty from the neglected topologies. If not, the inconsistency could be regarded as a warning to the QCD theories. Because the data were not complete, the analysis performed in [2] was limited to the O(λ) accuracy: the electroweak penguin amplitude Pew has been neglected for the B → ππ decays. The color-suppressed tree amplitude C, the color-suppressed electroweak penguin amplitude P c ew, and the tree annihilation amplitude T a have been neglected for the B → Kπ decays. In this work we shall improve the accuracy up to O(λ), since recent experimental progress has allowed this study. Moreover, we shall look for the solutions, in which the amplitudes of each topology from the B → ππ, Kπ modes are consistent with the approximate SU(3) flavor symmetry. If such solutions exist (there is no guarantee for the existence in this method), all the above data can be understood in a consistent way, and the determination of the weak phases φ2 and φ3 will be convincing. The B → ππ, Kπ old data have been investigated in [9, 10] based on the SU(3) flavor symmetry to some extent, and an extracted large Pew has been claimed to signal new physics. We shall point out that the large Pew is a consequence of the strong assumption of the SU(3) flavor symmetry and of the old data. Different prescriptions for taking into account SU(3) symmetry breaking effects have led to different extractions of amplitudes [9, 10, 11], while our exact solutions avoid this ambiguity. As shown below, the new data in fact imply only a large C, and all other amplitudes, including Pew, can be understood within the standard model. The most general topological-amplitude parametrization of the B → ππ decay amplitudes is written as √ 2A(B → ππ) = −T [ 1 + C T + Pew T e2 ]