Spectator scattering at NLO in non-leptonic B decays: Leading penguin amplitudes Original Research Article

We complete the computation of the 1-loop (image) corrections to hard spectator scattering in non-leptonic B decays at leading power in image by evaluating the penguin amplitudes. This extends the knowledge of these next-to-next-to-leading-order contributions in the QCD factorization formula for B decays to a much wider class of final states, including all pseudoscalar–pseudoscalar, pseudoscalar–vector, and longitudinally polarized vector–vector final states, except final states with η or image mesons. The new 1-loop correction is significant for the colour-suppressed amplitudes, but turns out to be strongly suppressed for the leading QCD penguin amplitude image. We provide numerical values of the phenomenological image and image amplitude ratios for the ππ, πρ and ρρ final states, and discuss corrections to several relations between electroweak penguin and tree amplitudes.