  Within the QCD factorization approach we compute the amplitudes for
annihilation channels of B mesons decays into final states containing two
pseudoscalar particles. These decays may be plagued by effects like
non-perturbative physics or breaking of the factorization hypothesis and imply,
at some extent, the introduction of an infrared cutoff in the calculation of
amplitudes. We compute the decays with the help of infrared finite gluon
propagators and coupling constants that were obtained in different solutions of
the QCD Schwinger-Dyson equations. These solutions yield a natural cutoff for
the amplitudes, and we argue that a systematic study of these B decays may
provide a test for the QCD infrared behavior.
