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 limi t for B decays to two light pseudoscalar mesons. and present some detailed calculations of radiative corrections at the order of alpha (s). We point o ut that the infrared finiteness of the vertex corrections in the chirally e nhanced power corrections requires twist-3 light-cone distribution amplitud es (LCDAs) of the light pseudoscalar symmetric. However, even in the symmet ric condition. there is also a logarithmic divergence from the end points o f 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 fre e 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.