Infrared Divergence and Twist-3 Distribution Amplitudes in QCD Factorization For $B\to PP$

Abstract

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 $a_i^p$ for $B\to \pi \pi$ at the next-to-leading order of ${\alpha }_s$ including chirally enhanced corrections. We also briefly discuss the divergence appeared in the hard spectator contributions.

Comments: 12 pages, 3 figures, A revised version to appear in Phys. Lett. B