Relations for Direct CP asymmetries \\in $B\to \rm PP$ and $B\to \rm PV$ decays

Abstract

The presence of additional strong phase from power corrections and other chirally enhanced terms makes it more difficult to predict direct CP asymmetries in two-body charmless B decays. In this talk, I would like to report on a recent work on QCD Factorisation and Power Corrections in Charmless B Decays. Using the measured branching ratios for $B\to \rm PV$, it is shown that power corrections in charmless B decays are probably large, at least for penguin dominated $\rm PV$ channels. Since the tree-penguin interference responsible for direct CP asymmetries in two-body charmless B decays are related by CKM factors and SU(3) symmetry, we find that, if power corrections other than the chirally enhanced power corrections and annihilation topology were negligible, QCD Factorisation would predict the direct CP asymmetry of $B \to π^+ π^-$ to be about 3 times larger than that of $B \to π^\pm K^\mp$, with opposite sign, in agreement with the latest measurement from Belle. Similar relations are also given for direct CP asymmetries in $B\to\rm PV$ .