$B_{s} \to (\rho, \omega, \phi) \eta^{(\prime)}$ Decays in the Perturbative QCD Approach

In this paper, we calculate the branching ratios and CP-violating asymmetries for $B_{s} \to (\rho^0,\omega, \phi) \eta^{(\prime)}$ decays in the perturbative QCD (pQCD) factorization approach. Numerically we found that (a) the pQCD predictions for the CP-averaged branching ratios are $Br(B_{s}\to\rho^0 \eta)\approx 0.07 \times 10^{-6}$, $Br(B_{s}\to\rho^{0}\eta^\prime) \approx 0.10 \times 10^{-6}$, $Br(B_{s} \to\omega\eta) \approx 0.02 \times 10^{-6}$, $Br(B_{s} \to\omega\eta^\prime) \approx 0.13 \times 10^{-6}$, $Br(B_{s} \to\phi\eta) \approx 2.7 \times 10^{-5}$ and $Br(B_{s} \to\phi\eta^\prime) \approx 2.0 \times 10^{-5}$; (b) the gluonic contributions are small in size: less than 3% for $B \to (\rho, \omega, \phi) \eta$ decays, and about 10% for $B \to (\rho, \omega, \phi) \eta^\prime$ decays; and (c) the pQCD predictions for the CP-violating asymmetries of the considered decays are generally not large in magnitude. The above predictions can be tested in the forthcoming LHC-b experiments at CERN.