$B\to \rho (\omega ,\varphi )\text{etap}$ Decays and NLO contributions in the pQCD Approach

By employing the perturbative QCD (pQCD) factorization approach, we calculated some important next-to-leading-order(NLO) contributions to the two-body charmless hadronic decays $B^{+}\to {\rho }^{+}{\eta }^{(\mathrm{\prime })}$ and $B^0 \to \rho^0(\omega, \phi) \eta^{(\prime)}$, induced by the vertex QCD corrections, the quark-loops as well as the chromo-magnetic penguins. From the numerical results and phenomenological analysis we find that (a) for $B^\pm \to \rho^\pm \etap$ decays, the partial NLO contributions to branching ratios are small in magnitude; (b) for $B^0\to {\rho }^0(\omega ,\varphi )\text{etap}$ decays, the NLO contributions can provide significant enhancements to the leading order predictions of their branching ratios; and © the pQCD predictions for the CP-violating asymmetries ${\text{acp}}^{dir}(B^{\pm }\to {\rho }^{\pm }\text{etap})$ are consistent with the data, while the predicted $\text{acp}(B^0\to {\rho }^0(\omega )\text{etap})$ are generally large in magnitude and could be tested by the forthcoming LHCb experiments.