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

TL;DR

This paper calculates branching ratios and CP asymmetries for B to K eta and eta' decays using the pQCD approach, including NLO corrections, and finds good agreement with experimental data.

Contribution

It provides the first comprehensive NLO pQCD predictions for these decay modes, enhancing understanding of their branching ratios and CP asymmetries.

Findings

NLO corrections significantly increase certain branching ratios.

Predicted CP asymmetries match well with experimental measurements.

NLO effects help explain the pattern of observed decay rates.

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 $\Delta S=\acp^{mix}(K^0_S \etar) - \sin{2\beta}$ in pQCD approach is also very small.