Extracting $α$ from the CP Asymmetry in $B^0 \to π^+ π^-$ Decays

Abstract

The extraction of the CKM angle $α$ from the asymmetry in $B^0 \to π^+π^-$ vs ${\bar B^0} \to π^+π^-$ 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 $π^+π^-$ 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.