v 1 1 4 O ct 1 99 6 TTP 96 - 49 hep - ph / 9610357 October 1996 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 b̄ → d̄ 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 modelindependent 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. Among the central goals of the planned dedicated B-physics experiments is the direct measurement of the angles α, β and γ arising in the unitarity triangle (UT) [1] of the Cabibbo–Kobayashi–Maskawa matrix (CKM matrix) [2]. Besides the “gold-plated” decay Bd → J/ψKS to determine sin(2β), the transition Bd → ππ plays a very important role to accomplish this task [3]. It is well-known that the time-dependent CP-violating asymmetry of this decay defined by aCP(t) ≡ Γ(B d(t) → π+π−)− Γ(B d(t) → ππ) Γ(B d(t) → π+π−) + Γ(B d(t) → π+π−) = A CP cos(∆Md t) +A CP sin(∆Md t) (1) probes the angle α of the UT, where ∆Md > 0 denotes the mass splitting of the B 0 d −B0 d mass eigenstates. In this expression we have separated direct from mixing-induced CPviolating contributions which are characterized by A CP ≡ 1− ∣