A Determination of the CKM - angle α using Mixing - induced CP Violation in the Decays B d → π + π − and B d → K 0 K̄ 0 ∗ Andrzej

We present a method of determining the CKM-angle α by performing simultaneous measurements of the mixing-induced CP asymmetries of the decays Bd → ππ and Bd → KK̄. The accuracy of our approach is limited by SU(3)-breaking effects originating from b̄ → d̄ss̄ QCD-penguin diagrams. Using plausible power-counting arguments we show that these uncertainties are expected to be of the same order as those arising through electroweak penguins in the standard Gronau-London-method in which α is extracted by means of isospin relations among B → ππ decay amplitudes. Therefore our approach, which does not involve the experimentally difficult mode Bd → ππ and is essentially unaffected by electroweak penguins, may be an interesting alternative to determine α. ∗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. CP-violating asymmetries arising in nonleptonic B-decays (see e.g. refs. [1]-[8]) will play a central role in the determination of the angles α, β and γ in the unitarity triangle [9, 10] at future experimental B-physics projects. Unfortunately, these asymmetries are in general not related to the CKM-angles in a clean way, but suffer from uncertainties originating from so-called penguins. These contributions preclude in particlular a clean determination of the CKM-angle α by measuring the mixing-induced CP-violating asymmetry Amix-ind CP (Bd → ππ). In a pioneering paper [11], Gronau and London have presented a method to eliminate the uncertainty in this determination of α that is related to QCD-penguins. It uses isospin relations among Bd → ππ, Bd → ππ and B → ππ decay amplitudes and requires besides a time-dependent study of Bd → ππ yielding Amix-ind CP (Bd → ππ) a measurement of the corresponding branching ratios. However, there are not only QCDbut also electroweak penguin operators. Although one would expect näıvely that electroweak penguins should only play a minor role in nonleptonic B-decays, there are certain transitions that are affected significantly by these operators which become important in the presence of a heavy top-quark. This interesting feature has first been pointed out in refs. [12]-[14] and has been confirmed later by the authors of refs. [15]-[17]. As has been stressed first by Deshpande and He [18], the influence of electroweak penguins on the extraction of α by using the standard Gronau-London-method [11] could also be sizable. A more elaborate analysis [19] shows, however, that this impact is expected to be rather small, at most a few per cent. In a recent paper [20] we have presented strategies for the experimental determination of electroweak penguin contributions to nonleptonic B-decays. These strategies allow in particular to control the electroweak penguin uncertainty affecting the extraction of the CKM-angle α in the Gronau-London-method [11]. Although this method of determining α is very clean from the theoretical point of view, it requires the measurement of the decay Bd → ππ which is rather difficult. The very recent analysis by Kramer and Palmer [21] indicates a branching ratio BR(Bd → ππ) < ∼O(10−6). Therefore, it is important to search for other methods that allow a clean determination of α. Such methods are also needed for overconstraining the shape of the unitarity triangle. Motivated by this experimental situation, Dunietz [22] has suggested an alternative way of extracting α that is based on the SU(3) flavour symmetry of strong interactions [23]-[27] and uses time-dependent measurements of the modes Bd → ππ and Bs → KK. However in view of the large B s–B̄ 0 s–mixing, the time-dependent analysis of the transition Bs → KK with the expected branching ratio at the O(10−5) level may be difficult as well. In this letter we would like to propose a different method of extracting α. In or-