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Branching Ratio and CP Asymmetry of $B \to ρη^{(\prime)}$ Decays in the Perturbative QCD Approach

In this paper,we calculate the branching ratios and CP-violating asymmetries for $B^0 \to ρ^0 η^{(\prime)}$ and $B^+\to ρ^+ \etap$ decays in the perturbative QCD factorization approach. In this approach, we not only calculate the usual factorizable contributions, but also evaluate the non-factorizable and annihilation type contributions. Besides the current-current operators, the contributions from the QCD and electroweak penguin operators are also taken into account. The theoretical predictions for the branching ratios are $Br(B^+ \to ρ^+ η^{(\prime)}) \approx 9 \times 10^{-6}$ and $Br(B^0 \to ρ^0 η^{(\prime)}) \approx 5 \times 10^{-8}$, which agree well with the measured values and currently available experimental upper limits. We also predict large CP-violating asymmetries in these decays: $A_{CP}^{dir}(ρ^\pm η)\approx -13 %$, $A_{CP}^{dir}(ρ^\pm η^\prime)\approx -18 %$, $A_{CP}^{dir}(ρ^0 η)\approx -41%$, $A_{CP}^{dir}(ρ^0 η^\prime)\approx -27%$, $A_{CP}^{mix}(ρ^0 η)\approx +25%$, and $A_{CP}^{mix}(ρ^0 η^\prime) \approx +11%$, which can be tested by the current or future B factory experiments.