A Determination of the CKM-angle $\alpha$ using Mixing-induced CP Violation in the Decays $B_d\to {\pi }^{+}{\pi }^{-}$ and $B_d\to K^0{\bar{K}}^0$

Abstract

We present a method of determining the CKM-angle $\alpha$ by performing simultaneous measurements of the mixing-induced CP asymmetries of the decays $B_d\to {\pi }^{+}{\pi }^{-}$ and $B_d\to K^0{\bar{K}}^0$. The accuracy of our approach is limited by $SU(3)$-breaking effects originating from $\bar{b}\to \bar{d}s\bar{s}$ 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 $\alpha$ is extracted by means of isospin relations among $B\to \pi \pi$ decay amplitudes. Therefore our approach, which does not involve the experimentally difficult mode $B_d\to {\pi }^0{\pi }^0$ and is essentially unaffected by electroweak penguins, may be an interesting alternative to determine $\alpha$.

12 pages, LaTeX, Figure not included

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