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Effect of Hairpin Diagram on Two-body Nonleptonic B Decays and CP Violation

A careful quark-diagram analysis shows that a number of two-body nonleptonic $B$ decays can occur through the so-called hairpin diagram, a QCD loop-induced graph different from penguin in final-state hadronization of valence quarks. Using the two-loop renormalization-group-improved effective Hamiltonian and the naive factorization approximation, we demonstrate the effect of the hairpin diagram on decay rates and $CP$ asymmetries for a few interesting channels such as $B^{0}_{d},\bar{B}^{0}_{d} \rightarrow ψK_{S}$ and $B^{\pm}_{u}\rightarrow ϕK^{\pm}$. Branching ratios of some pure hairpin decay modes, e.g., $B^{-}_{u}\rightarrow ϕπ^{-},ϕρ^{-}$ and $\bar{B}^{0}_{d}\rightarrow ϕπ^{0},ϕρ^{0}, ϕω, ϕη,$ etc., are estimated to be on the order of $10^{-7}$.