Branching ratio and CP asymmetry of [formula omitted] decays in the perturbative QCD approach

Abstract

We calculate the branching ratios and CP-violating asymmetries for B 0 → π 0 η ( ′ ) and B + → π + η ( ′ ) 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 + → π + η ) ≈ 4.1 × 10 −6 , Br ( B + → π + η ′ ) ≈ 2.4 × 10 −6 , and Br ( B 0 → π 0 η ( ′ ) ) ≈ 0.2 × 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 ± η ( ′ ) ) ∼ A CP dir ( π 0 η ( ′ ) ) ∼ − 0.35 , and A CP mix ( π 0 η ( ′ ) ) ∼ 0.67 , but with large errors. The pQCD prediction for A CP dir ( π ± η ) ( A CP dir ( π ± η ′ ) ) has the same (opposite) sign with the primary measured values. Further improvements in both theory and experiments are needed to clarify this discrepancy.