Extracting α from the CP asymmetry in ${\mathit{B}}^0$→${\mathrm{\pi }}^{+}$${\mathrm{\pi }}^{\mathrm{-}}$ decays

The extraction of the CKM angle α from the asymmetry in ${\mathit{B}}^0$→${\mathrm{\pi }}^{+}$ ${\mathrm{\pi }}^{\mathrm{-}}$ versus B${\mathrm{¯}}^0$→${\mathrm{\pi }}^{+}$ ${\mathrm{\pi }}^{\mathrm{-}}$ 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 ${\mathit{B}}^0$ and B${\mathrm{¯}}^0$ decays to ${\mathrm{\pi }}^{+}$ ${\mathrm{\pi }}^{\mathrm{-}}$ from untagged events. These measurements, together with the magnitudes and relative phase of the tree and penguin diagrams, can in principle completely determine α, free of discrete ambiguities. We perform an error analysis on α given assumptions on the values and uncertainties of both the measurements and theoretical inputs. ©1996 The American Physical Society.