Power Corrections in Charmless Nonleptonic B-Decays: Annihilation is   Factorizable and Real
  We classify LambdaQCD/mb power corrections to nonleptonic B-> M1 M2 decays, where M1 and M2 are charmless non-isosinglet mesons. Using recent developments in soft-collinear effective theory, we prove that the leading contributions to annihilation amplitudes of O[alphas(mb) LambdaQCD/mb] are real. The leading annihilation amplitudes depend on twist-2 and twist-3 three parton distributions. A complex nonperturbative parameter from annihilation first appears at O[alphas^2(sqrt{Lambda mb}) LambdaQCD/mb]. ``Chirally enhanced'' contributions are also factorizable and real at lowest order. Thus, incalculable strong phases are suppressed in annihilation amplitudes, unless the alphas(sqrt{Lambda mb}) expansion breaks down. Modeling the distribution functions, we find that (11 +- 9)% and (15 +- 11)% of the absolute value of the measured B-> K- pi+ and B-> K- K0 penguin amplitudes come from annihilation. This is consistent with the expected size of power corrections. 
Christian M. Arnesen, Zoltan Ligeti, Ira Z. Rothstein, Iain W. Stewart