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

Abstract

We complete the computation of the 1-loop (alpha_s^2) corrections to hard spectator scattering in non-leptonic B decays at leading power in Lambda/m_b 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 eta or eta' 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 alpha_4^p. We provide numerical values of the phenomenological P/T and C/T amplitude ratios for the pi pi, pi rho and rho rho final states, and discuss corrections to several relations between electroweak penguin and tree amplitudes.