Extracting $\alpha$ from the CP Asymmetry in $B^0\to {\pi }^{+}{\pi }^{-}$ Decays

Abstract

The extraction of the CKM angle $\alpha$ from the asymmetry in $B^0\to {\pi }^{+}{\pi }^{-}$ vs ${\bar{B}}^0\to {\pi }^{+}{\pi }^{-}$ suffers from a currently unknown penguin contribution. Experimentally, one can determine the magnitude and phase of the CP asymmetry from a time-dependent analysis of tagged events, and the average rate for $B^0$ and ${\bar{B}}^0$ decays to ${\pi }^{+}{\pi }^{-}$ from untagged events. These measurements, together with the magnitudes and relative phase of the tree and penguin diagrams, can in principle completely determine $\alpha$, free of discrete ambiguities. We perform an error analysis on $\alpha$ given assumptions on the values and uncertainties of both the measurements and theoretical inputs.

Comments: 18 pages latex, 9 eps files