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

We complete the computation of the 1-loop (αs) corrections to hard spectator scattering in non-leptonic B decays at leading power in Λ/mb by evaluating the penguin amplitudes. This extends the knowledge of these next-to-next-to-leadingorder 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′ 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 αp4. We provide numerical values of the phenomenological P/T and C/T amplitude ratios for the ππ, πρ and ρρ final states, and discuss corrections to several relations between electroweak penguin and tree amplitudes. Address after 01 October 2006: Arnold Sommerfeld Center, Department für Physik, LudwigMaximilians-Universität München, Theresienstraße 37, D-80333 München, Germany