Possibility of large electro - weak penguin contribution in B → Kπ modes

We discuss about a possibility of large electro-weak penguin contribution in B → Kπ from recent experimental data. The several relations among the branching ratios which realize when the contributions from tree type and electro-weak penguin are small compared with the gluon penguin and can be treated as the expansion parameters do not satisfy the data. The difference comes from the r terms which is the square of the ratio with the gluon penguin and the main contribution comes from electro-weak penguin. We find that the contribution from electro-weak penguin may be large to explain the experimental data. If the magnitude estimated from experiment is quite large compared with the theoretical estimation, then it may be including some new physics effects. Emails: [email protected] One of the main targets at the B factories is to determine the all CP angles in the unitarity triangles of the Cabbibo-Kobayashi-Maskawa (CKM) matrix [1]. φ1[2] as one of the angles has already been measured and established the CP violation in the B meson system by Belle[3] and BaBar[4] collaborations. The next step is to measure the remaining angles. The canonical decay modes for measuring φ2 and φ3 are B 0 d → ππ and B → DK respectively but the methods have some difficulties to extract cleanly the angles. To avoid the difficulty, isospin relation[6] and SU(3) relation including B → Kπ modes [7]-[10] are being considered as a method to extract the weak phases. B → Kπ modes has been also measured[5] and they will be useful informations to understand the CP violation through the KM phases. If we can directory solve about these modes, it is very elegant way to determine the parameters and the weak phase. However we can not do so because there are too many parameters in B → Kπ modes to extract the weak phases. So we need understand these modes step by step. To understand the weak phase through this mode, there are several approaches by diagram decomposition[7]-[13], QCD factorization[14] and pQCD[15] and so on. The contributions including the weak phase φ3 come from tree type diagrams which has CKM suppression factor and they are usually dealt with small parameter compared with gluon penguin. If we can deal the contributions except for gluon penguin with the small parameters, then, there are several relations among the averaged branching ratios of B → Kπ modes. For example, Br(Kπ)/2Br(Kπ) ≈ 2Br(Kπ)/Br(Kπ) [14] et al. However, the recent experiment does not seem to satisfy them so well. When we reconsider these modes to compare with the data, we find that the role of a color favored electro-weak penguin may be important to explain the difference between the relations and the experimental data. The color favored electro-weak penguin diagram is included in B → Kπ and B → Kπ and the data of the branching ratio are slightly larger than half of B → Kπ, where the 1/2 comes from the difference of π and π in final state. So we need to know the informations about the electro-weak penguin contributions in B → Kπ decay modes to understand about the effect from the weak phases. The role was pointed out and the magnitude was estimated in several works[14]. They said that the ratio between gluon and electro-weak penguins is about 0.14 as the central value but the experimental data may suggest that the magnitude seem to be slightly larger than the estimation. If there is quite large deviation in the contribution from the electro-weak penguin, it may suggest a possibility of new physics in these modes. In B → KSπ, we can consider to use the time-dependent CP asymmetry to extract the weak phase. However the mode has the electro-weak penguin diagram so that one must remove the contribution to extract φ3. And we have to check whether extracting φ3 is possible or not. To do so, it is important to reconsider about the electro-weak penguin. In this work, we consider how large contribution from the electro-weak penguins from only experimental data. The decay amplitudes of B → Kπ are A ≡ A(B → Kπ) = 