Penguin corrections and strong phases in a time-dependent analysis of $B^0_{d} \to π^+ π^-$

From a time-dependent analysis of the decay $B^0_{d} \to \pi^+ \pi^-$ 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 $B^0_{d} \to J/\psi K_S$, is used to parameterize the value of $A_P/A_T$ and the corresponding penguin correction to the observed asymmetry in $B^0_{d} \to \pi^+ \pi^-$.