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

Abstract

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 $B_d^0,{\bar{B}}_d^0\to \psi K_S$ and $B_u^{\pm }\to \varphi K^{\pm }$. Branching ratios of some pure hairpin decay modes, e.g., $B_u^{-}\to \varphi {\pi }^{-},\varphi {\rho }^{-}$ and ${\bar{B}}_d^0\to \varphi {\pi }^0,\varphi {\rho }^0,\varphi \omega ,\varphi \eta ,$ etc., are estimated to be on the order of $10^{-7}$.

14 pages (Latex, 2 figures available), BIHEP-TH-93-25 (accepted for publication in Phys. Lett. B)

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