QCD factorization for B→PP -: art. no. 014036

In this work, we give a detailed discussion for QCD factorization involved in the complete chirally enhanced power corrections in the heavy quark limit for B decays to two light pseudoscalar mesons. and present some detailed calculations of radiative corrections at the order of alpha (s). We point out that the infrared finiteness of the vertex corrections in the chirally enhanced power corrections requires twist-3 light-cone distribution amplitudes (LCDAs) of the light pseudoscalar symmetric. However, even in the symmetric condition. there is also a logarithmic divergence from the end points of the twist-3 LCDAs in the hard spectator scattering. We point out that the decay amplitudes of B --> PP predicted by QCD factorization are really free of the renormalization scale dependence, at least at the order of alpha (s). At last, we briefly compare the QCD factorization with the generalized factorization and PQCD method.