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In this paper,we calculate the branching ratios and CP-violating asymmetriesfor $B^0 \to \rho^0 \eta^{(\prime)}$ and $B^+\to \rho^+ \etap$ decays in theperturbative QCD factorization approach. In this approach, we not onlycalculate the usual factorizable contributions, but also evaluate thenon-factorizable and annihilation type contributions. Besides thecurrent-current operators, the contributions from the QCD and electroweakpenguin operators are also taken into account. The theoretical predictions forthe branching ratios are $Br(B^+ \to \rho^+ \eta^{(\prime)}) \approx 9 \times10^{-6}$ and $Br(B^0 \to \rho^0 \eta^{(\prime)}) \approx 5 \times 10^{-8}$,which agree well with the measured values and currently available experimentalupper limits. We also predict large CP-violating asymmetries in these decays:$A_{CP}^{dir}(\rho^\pm \eta)\approx -13 %$, $A_{CP}^{dir}(\rho^\pm\eta^\prime)\approx -18 %$, $A_{CP}^{dir}(\rho^0 \eta)\approx -41%$,$A_{CP}^{dir}(\rho^0 \eta^\prime)\approx -27%$, $A_{CP}^{mix}(\rho^0\eta)\approx +25%$, and $A_{CP}^{mix}(\rho^0 \eta^\prime) \approx +11%$, whichcan be tested by the current or future B factory experiments.Comment: 29 pages, 9 ps figures, more phenomenological discussions added,  scale dependence of computed observables are considered, typos corrected, the  figures and conclusions remain unchange

physical review. d. particles, fields, gravitation, and cosmology/physical review. d, particles, fields, gravitation, and cosmology

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Branching ratio andCPAsymmetry ofB→ρη(′)decays in the perturbative QCD approach