QCD factorization for B → ππ decays:: Strong phases and CP violation in the heavy quark

We show that, in the heavy quark limit, the hadronic matrix elements that enter B meson decays into two light mesons can be computed from first principles, including "nonfactorizable" strong interaction corrections, and expressed in terms of form factors and meson light-cone distribution amplitudes. The conventional factorization result follows in the limit when both power corrections in 1/m(b) and radiative corrections in alpha(s) are neglected. We compute the order-alpha(s) corrections to the decays B-d --> pi(+)pi(-), B-d --> pi(0) pi(0), and B+ --> pi(+) pi(0) in the heavy quark limit and briefly discuss the phenomenological implications for the branching ratios, strong phases and CP violation.