NNLO vertex corrections in charmless hadronic B decays: Imaginary part

We compute the imaginary part of the 2-loop vertex corrections in the QCD factorization framework for hadronic two-body decays as B→ππ. This completes the NNLO calculation of the imaginary part of the topological tree amplitudes and represents an important step towards an NNLO prediction of direct CP asymmetries in QCD factorization. Concerning the technical aspects, we find that soft and collinear infrared divergences cancel in the hard-scattering kernels which demonstrates factorization at the 2-loop order. All results are obtained analytically including the dependence on the charm quark mass. The numerical impact of the NNLO corrections is found to be significant, in particular they lead to an enhancement of the strong phase of the colour-suppressed tree amplitude.