$B_{(s)}\to {\eta }_c(P,V)$ decays and effects of the next-to-leading order contributions in the perturbative QCD approach

By employing the perturbative QCD (PQCD) factorization approach, we studied the sixteen $B\mathrm{/}{B}_s\to {\eta }_c(\pi ,K,{\eta }^{(\mathrm{\prime })},\rho ,K^{\ast },\omega ,\varphi )$ decays with the inclusion of the currently known next-to-leading order (NLO) contributions. We found the following main points: (a) for the five measured $B \to \eta_c (K,K^*)$and$B_s\to \eta_c\phi$ decays, the NLO contributions can provide $(80-180)\mathrm{\%}$ enhancements to the leading order (LO) PQCD predictions of their branching ratios, which play an important role to help us to interpret the data; (b) for the seven ratios $R_{1,\cdots ,7}$ of the branching ratios defined among the properly selected pair of the considered decay modes, the PQCD predictions for the values of $R_{3,4,5}$ agree well with those currently available measurements from BaBar and Belle Collaboration; © for $B^0 \to \eta_c K_S^0$ decay, the PQCD predictions for both the direct and mixing induced CP asymmetries do agree very well with the measured values within errors; and (d) the PQCD predictions for ratios $R_{1,2}$ and $R_{6,7}$ also agree with the general expectations and will be tested by the future experiments.