Power Corrections in Charmless B Decays

In this paper, we focus on the role of power corrections in QCD factorization(QCDF) method in charmless two-body nonleptonic $B$ meson decays. We use the ratio of the branching fraction of $B^+ \to \pi^+ K^{\ast 0}$ to that of $B^0 \to \pi^- \rho^+$, for which the theoretical uncertainties are greatly reduced, to show clearly that the power corrections in charmless B decays are probably large. With other similar ratios considered, for example, for the $B^0 \to K^- \rho^+$ decay, it is very likely that, among various sources of power corrections, annihilation topology plays an indispensable role at least for penguin dominated $\rm PV$ channels. We also consider some selective ratios of direct CP asymmetries. Among these, we find that, if power corrections other than the chirally enhanced power corrections and annihilation topology were negligible, QCDF would predict the direct CP asymmetry of $B \to \pi^+ \pi^-$ to be about 3 times larger than that of $B \to \pi^\pm K^\mp$, with opposite sign. Experimentally any significant deviation from this prediction would suggest either new physics or possibly the importance of long-distance rescattering effects.