A Further Study of $CP$ Asymmetries in Pure Penguin-induced $B^{\pm}_{u}$ Decays

Abstract

We make a further study of $CP$ asymmetries in the pure penguin-induced decay modes $B^{-}_{u}\rightarrow K^{(*)0} + K^{(*)-}$ and $B^{-}_{u} \rightarrow \bar{K}^{(*)0} + (\pi^{-}, \rho^{-}, a^{-}_{1})$ by using the two-loop renormalization-group-improved effective Hamiltonian and factorization approximation. Different from the previous results obtained without QCD corrections, the $CP$ asymmetries in each of the two groups are enhanced and classified with their respective factorization coefficients. A sum over the pure penguin modes of each group is proposed to obtain an effective branching ratio and a {\it weighted-mean} signal of $CP$ violation, which should be statistically significant for experimental observation.