Infrared divergence and twist-3 distribution amplitudes in QCD factorization for B→PP

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 final light pseudoscalar mesons described by leading twist and twist-3 distribution amplitudes. We find that chirally enhanced corrections can be included consistently in the framework of QCD factorization only if the twist-3 distribution amplitudes are symmetric. We then give explicit expressions of aip for B→ππ at the next-to-leading order of αs including chirally enhanced corrections. We also briefly discuss the divergence appeared in the hard spectator contributions.