Penguin zoology in B → ππ and the extraction of the CKM angle α

We reanalyze the decay Bd → π+π− without assuming dominance of QCD penguins with internal top-quark exchanges. In that case the weak phase of the b → d QCD penguin amplitude is not related in a simple way to the CKM angle β. Nevertheless it is still possible to extract the CKM angle α in a transparent and almost model-independent way from the time-dependent CP-violating asymmetry of the transition Bd → π+π−. Aside from that CP asymmetry this approach needs as an input only amplitudes of decays with branching ratios of order 10−5 and will thus be well within reach at future B-factories.