QCD Factorization For B Decays To Two Light Pseudoscalars Including   Chirally Enhanced Corrections
  Since b quark mass is not asymptotically large, chirally enhanced corrections which arise from twist-3 wave functions may be important in B decays. We thus evaluate the hadronic matrix elements with the emitted meson described by leading twist and twist-3 distribution amplitudes $\Phi_p(x)$. After summing over the four "vertex correction" diagrams, we obtain the results with infrared finiteness which shows that chirally enhanced corrections arise from $\Phi_p(x)$ can be consistently included in QCD factorization. We also briefly discuss the contributions from "hard spectator" diagrams. 
Dongsheng Du, Deshan Yang and Guohuai Zhu