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

Abstract

We calculate the branching ratios and CP-violating asymmetries for $B^0\to {\pi }^0{\eta }^{(\prime )}$ and $B^{+}\to {\pi }^{+}{\eta }^{(\prime )}$ decays in the perturbative QCD (pQCD) factorization approach here. 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 pQCD results for the CP-averaged branching ratios are $Br(B^{+}\to {\pi }^{+}\eta )\approx 4.1\times 10^{-6}$, $Br(B^{+}\to {\pi }^{+}{\eta }^{\prime })\approx 2.4\times 10^{-6}$, and $Br(B^0\to {\pi }^0{\eta }^{(\prime )})\approx 0.2\times 10^{-6}$, which agree very well with the measured values or currently available experimental upper limits. We also predict large CP-violating asymmetries in these decays: $A_{CP}^{dir}({\pi }^{\pm }\text{etap})\sim A_{CP}^{dir}({\pi }^0\text{etap})\sim -0.35$, and $A_{CP}^{mix}({\pi }^0\text{etap})\sim 0.67$, but with large errors. The pQCD prediction for $A_{CP}^{dir}({\pi }^{\pm }\eta )$ ($A_{CP}^{dir}({\pi }^{\pm }{\eta }^{\prime }))$ has the same (opposite) sign with the primary measured values. Further improvements in both theory and experiments are needed to clarify this discrepancy.

Comments: 28 pages, 8 figures, several typos corrected