Testing the dynamics of B -> \pi\pi and constraints on \alpha

Abstract

In charmless nonleptonic B decays to \pi\pi or \rho\rho, the "color allowed" and "color suppressed" tree amplitudes can be studied in a systematic expansion in \alphas(mb) and \Lambda/mb. At leading order in this expansion their relative strong phase vanishes. The implications of this prediction are obscured by penguin contributions. We propose to use this prediction to test the relative importance of the various penguin amplitudes using experimental data. The present B->\pi\pi data suggest that there are large corrections to the heavy quark limit, which can be due to power corrections to the tree amplitudes, large up-quark penguin amplitude, or enhanced weak annihilation. Because the penguin contributions are smaller, the heavy quark limit is more consistent with the B->\rho\rho data, and its implications may become important for the extraction of \alpha from this mode in the future.