Spectator scattering at NLO in non-leptonic B decays: Tree amplitudes

We compute the I-loop (alpha(2)(s)) correction to hard spectator scattering in non-leptonic B decay tree amplitudes. This forms part of the NNLO contribution to the QCD factorization formula for hadronic B decays, and introduces a new rescattering phase that corrects the leading-order result for direct CP asymmetries. Among the technical issues, we discuss the cancellation of infrared divergences, and the treatment of evanescent four-quark operators. The infrared finiteness of our result establishes factorization of spectator scattering at the I-loop order. Depending on the values of hadronic input parameters, the new I-loop correction may have a significant impact on tree-dominated decays such as B -> pi pi.