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Semi-inclusive B Decays and Direct CP Violation in QCD Factorization

We have systematically investigated the semi-inclusive B decays B->MX, which are manifestations of the quark decay b->Mq, within the framework of QCD-improved factorization. These decays are theoretically clean and have distinctive experimental signatures. We focus on a class of these that do not require any form factor information and therefore may be especially suitable for extracting information on the angles $α$ and $γ$ of the unitarity triangle. The nonfactorizable effects, such as vertex-type and penguin-type corrections to the two-body b decay and hard spectator corrections to the 3-body decay are calculable in the heavy quark limit. QCD factorization is applicable when the emitted meson is a light meson or a charmonium. We discuss the issue of the CPT constraint on partial rate asymmetries. The strong phase coming from final-state rescattering due to hard gluon exchange between the final states can induce large rate asymmetries for tree-dominated color-suppressed modes $(π^0,ρ^0,ω)X_{\bar s}$. The nonfactorizable hard spectator interactions in the 3-body decay, though phase-space suppressed, are extremely important for the tree-dominated modes $(π^0,ρ^0,ω)X_{\bar s}, ϕX$, $J X_s,J X$ and the penguin-dominated mode $ωX_{s\bar s}$. In fact, they are dominated by the hard spectator corrections. Our result for ${\cal B} (B\to J/ψX_s)$ is in agreement with experiment. The semi-inclusive decay modes: $B^0_s\to (π^0,ρ^0,ω)X_{\bar s}$, $ρ^0X_{s\bar s}$, $B^0\to(K^-X,K^{*-}X)$ and $B^-\to (K^0X_s,K^{*0}X_s)$ are the most promising ones in searching for direct CP violation. In fact, they have branching ratios of order $10^{-6}-10^{-4}$ and CP rate asymmetries of order $(10-40)%$.