Large Penguin effects in the CP Asymmetry of B0d ->pi+pi-

Abstract

Penguin effects in the CP asymmetries of $B^0_d\rightarrow \pi^+\pi^-$ , $\bd\rightarrow\rho^{\pm}\pi^{\mp}$ and $\bd\rightarrow a^{\pm}_1 \pi^{\mp}$ are studied as function of the CKM unitarity triangle $\alpha$. Despite a fairly small penguin amplitude, it leads to quite sizable uncertainties in the determination of $\sin(2\alpha)$ from all but very large asymmetries. This effect is maximal for vanishing final state interaction phases, for which it can cause, for instance, an asymmetry of 40\%\ if $\alpha=\pi/2$.