Penguin corrections and strong phases in a time-dependent analysis of $B_d^0\to {\pi }^{+}{\pi }^{-}$

Abstract

From a time-dependent analysis of the decay $B_d^0\to {\pi }^{+}{\pi }^{-}$ and using a model-dependent $A_P/A_T$ ratio of the penguin-to-tree amplitudes contributing to the decay, both the weak phase $\alpha$ and the strong phase shift difference $\delta$ can be extracted from the data. The value of the weak phase $\beta$, expected to be measured from the decay $B_d^0\to J/\psi K_S$, is used to parameterize the value of $A_P/A_T$ and the corresponding penguin correction to the observed asymmetry in $B_d^0\to {\pi }^{+}{\pi }^{-}$.

Comments: revised bibliography, 23 pages, 9 Postscript figures, Latex2e