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

Abstract

In this paper,we calculate the branching ratios and CP-violating asymmetries for $B^0\to {\rho }^0{\eta }^{(\prime )}$ and $B^{+}\to {\rho }^{+}\text{etap}$ 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 $Br(B^{+}\to {\rho }^{+}{\eta }^{(\prime )})\approx 9\times 10^{-6}$ and $Br(B^0\to {\rho }^0{\eta }^{(\prime )})\approx 5\times 10^{-8}$, which agree well with the measured values and currently available experimental upper 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 $A_{CP}^{mix}({\rho }^0{\eta }^{\prime })\approx +11$, which can be tested by the current or future B factory experiments.

Comments: 29 pages, 9 ps figures, more phenomenological discussions added, scale dependence of computed observables are considered, typos corrected, the figures and conclusions remain unchanged