Extraction of $α$ From the CP Asymmetry in B^0/\bar B^0 --> pi+ pi- Decays

Abstract

The influence of strong and electroweak penguin amplitudes in $B/ \bar B \rightarrow π^+π^-$ is investigated in connection with the determination of the unitarity triangle angle $α$ of the CKM matrix. A relation between the observable asymmetry, the angle $α$, and the penguin amplitude is established. A model calculation of the penguin amplitude shows that the CP asymmetry in $B^{0}\rightarrow π^{+}π^{-}$ decays is only mildly influenced by the penguin amplitudes. Experimental limits on pure penguin and penguin dominated processes are consistent with the model. This information also suggests in a rather model independent way that penguin amplitudes will not be a serious complicating factor in the determination of $α$ from the $π^{+}π^{-}$ time dependent asymmetry.

15 pages, Latex, three figures available upon request