Branching ratios and CP asymmetries of $B\to K{\eta }^{(\prime )}$ decays in the pQCD approach

Abstract

We calculate the branching ratios and CP violating asymmetries of the four $B \to K \etap$ 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 chromo-magnetic penguins are also taken into account. The NLO pQCD predictions for the CP-averaged branching ratios are $Br(B^{+}\to K^{+}\eta )\approx 3.2\times 10^{-6}$, $Br(B^\pm \to K^\pm \etar) \approx 51.0 \times 10^{-6}$, $Br(B^0\to K^0\eta )\approx 2.1\times 10^{-6}$, and $Br(B^0 \to K^0 \etar) \approx 50.3 \times 10^{-6}$. The NLO contributions can provide a 70% enhancement to the LO $Br(B \to K \etar)$, but a 30% reduction to the LO $Br(B\to K\eta )$, which play the key role in understanding the observed pattern of branching ratios. The NLO pQCD predictions for the CP-violating asymmetries, such as $\acp^{dir} (K^0_S \etar) \sim 2.3% $ and $\acp^{mix}(K^0_S \etar)\sim 63%$, agree very well with currently available data. This means that the deviation $ΔS=\acp^{mix}(K^0_S \etar) - \sin{2β}$ in pQCD approach is also very small.

31 pages, 11 ps/eps figures, typos corrected. A little modification

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• Branching Ratio and CP Asymmetry of $B_s\to \rho (\omega )K$ Decays in the Perturbative QCD Approach
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• Hadronic B decays
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