Towards the Control over Electroweak Penguins in Nonleptonic B - Decays ∗ Andrzej

We present strategies for determining electroweak penguins from experimental data. Using the CKM-angle γ as one of our central inputs and making some reasonable approximations, we show that the b̄ → s̄ electroweak penguin amplitude can be determined in a two-step procedure involving i) BR(B → πK), BR(B− → π0K−), BR(B → πK) and ii) either BR(B d → π −K+), BR(B̄ d → π +K−) or aCP(t) of the mode Bs → K +K−. The determination employing the B → πK transitions is not affected by SU(3)-breaking effects. Relating the b̄ → s̄ electroweak penguin amplitude to the b̄ → d̄ case through SU(3) symmetry arguments, we are in a position to estimate the electroweak penguin uncertainty affecting the extraction of the CKM-angle α by using isospin relations among B → ππ decays. Our results allow in principle the determination of CKM-phases in a variety of B-decays. ∗Supported in part by the German Bundesministerium für Bildung und Forschung under contract 06–TM–743 and by the CEC science project SC1–CT91–0729. During the last two years there has been a considerable interest in the role of electroweak penguin contributions in non-leptonic B-decays. Since the Wilson coefficients of the corresponding local operators increase strongly with the top-quark mass, it has been found [1, 2, 3] that the role of the electroweak penguins can be substantial in certain decays. This is for instance the case of the decay B− → K−Φ [1], which exhibits sizable electroweak penguin effects. More interestingly, there are even some channels, such as B− → π−Φ [2] and Bs → π Φ [3], which are dominated completely by electroweak penguin contributions and which should, thus, allow interesting insights into the physics of the corresponding operators. In this respect, the decay Bs → π Φ (or similar transitions such as Bs → ρ Φ) is very promising due to its special isospin-, CKMand colour-structure [3]. As the branching ratio of this mode is expected to be of O(10−7), it will unfortunately be rather difficult to analyze this decay experimentally. The electroweak penguin effects discussed in refs. [1, 3] have been confirmed by other authors [4]-[6]. In the foreseeable future the branching ratios ofO(10−5) and possiblyO(10−6) will be experimentally available and it is important to ask about the role of electroweak penguin effects in the corresponding channels. In particular, the question arises whether the usual strategies for the determination of the CKM-phases are affected by the presence of the electroweak penguin contributions. It is evident that the pure tree diagram decays do not receive any contributions from electroweak penguins. Consequently, the very clean method for the determination of the phase γ proposed by Gronau and Wyler [7] involving charged B-decays of the type B± → DK± (see also ref. [8]) remains unaffected by these new contributions. This applies also to the γ-determination proposed by Aleksan et al. [9] which uses a measurement of the time-dependent decay rates of the transitions Bs → D ± s K ∓. Similar comments apply to the “gold-plated” decay Bd → ψKS in which the electroweak penguins having the same phase as the leading tree contribution do not obscure a very clean determination of the phase β. The situation concerning the α-determination by means of the isospin relations among B → ππ decays proposed by Gronau and London [10] is more involved, however. As pointed out first by Deshpande and He [11], the impact of electroweak penguins on this determination could be sizable. A closer look [12] shows, however, that this impact is rather small, at most a few %. On the other hand, it is now well accepted [11, 12] that the electroweak penguins should have a considerable impact on the methods proposed last year by Gronau, Hernández, London and Rosner [13]-[18] to measure both weak and strong phases by using SU(3) triangle relations among B → {ππ, πK,KK̄} decays and making certain plausible dynamical assumptions (e.g. neglect of annihilation topologies). While this point has been shown explicitly in ref. [11], a systematic classification of