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

Abstract

We calculate the branching ratios and CP-violating asymmetries for $B^0 \to π^0 η^{(\prime)}$ and $B^+\to π^+ η^{(\prime)}$ 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 $Br(B^+ \to π^+ η) \approx 4.1 \times 10^{-6}$, $Br(B^+ \to π^+ η^\prime) \approx 2.4 \times 10^{-6}$, and $Br(B^0 \to π^0 η^{(\prime)}) \approx 0.2 \times 10^{-6}$, 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}(π^\pm \etap)\sim A_{CP}^{dir}(π^0 \etap)\sim -0.35 $, and $A_{CP}^{mix}(π^0 \etap)\sim 0.67$, but with large errors. The pQCD prediction for $A_{CP}^{dir}(π^\pm η)$ ($A_{CP}^{dir}(π^\pm η^\prime))$ has the same (opposite) sign with the primary measured values. Further improvements in both theory and experiments are needed to clarify this discrepancy.