Branching ratios and CP asymmetries of B -> K eta(()'()) decays in the perturbative QCD approach

We calculate the branching ratios and CP-violating asymmetries of the four B -> K eta(()'()) decays in the perturbative QCD (pQCD) factorization approach. Besides the full leading-order contributions, the partial next-to-leading-order (NLO) contributions from the QCD vertex corrections, the quark-loops, and the chromomagnetic penguins are also taken into account. The NLO pQCD predictions for the CP-averaged branching ratios are Br(B+ -> K+eta) approximate to 3.2 X 10(-6), Br(B-+/- -> K-+/- eta') approximate to 51.0 x 10(-6), Br(B-0 -> K-0 eta) approximate to 2.1 X 10(-6), and Br(B-0 -> K-0 eta') approximate to 50.3 X 10(-6). The NLO contributions can provide a 70% enhancement to the LO Br(B -> K eta'), but a 30% reduction to the LO Br(B -> K eta), which play the key role in understanding the observed pattern of branching ratios. The NLO pQCD predictions for the CP-violating asymmetries, such as A(CP)(dir) (K-S(0)eta') similar to 2.3% and A(CP)(mix) (K-S(0)eta') similar to 63%, agree very well with currently available data. This means that the deviation Delta S A(CP)(mix) (K-S(0)eta') - sin2 beta in pQCD approach is also very small.