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 $B\to K\text{etap}$ 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 $Br(B^{+}\to K^{+}\eta )\approx 3.2\times 10^{-6}$, $Br(B^{\pm }\to K^{\pm }\text{etar})\approx 51.0\times 10^{-6}$, $Br(B^0\to K^0\eta )\approx 2.1\times 10^{-6}$, and $Br(B^0\to K^0\text{etar})\approx 50.3\times 10^{-6}$. The NLO contributions can provide a 70% enhancement to the LO $Br(B\to K\text{etar})$, 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 ${\text{acp}}^{dir}(K_S^0\text{etar})\sim 2.3$ and ${\text{acp}}^{mix}(K_S^0\text{etar})\sim 63$, agree very well with currently available data. This means that the deviation $\Delta S={\text{acp}}^{mix}(K_S^0\text{etar})-\sin 2\beta$ in pQCD approach is also very small.

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