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

We complete the computation of the 1-loop (αs2) corrections to hard spectator scattering in non-leptonic B   decays at leading power in Λ/mbΛ/mb 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 η′η′ 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 α4p. We provide numerical values of the phenomenological P/TP/T and C/TC/T amplitude ratios for the ππ, πρ and ρρ final states, and discuss corrections to several relations between electroweak penguin and tree amplitudes.