$B_{s} \to (ρ, ω, ϕ) η^{(\prime)}$ Decays in the Perturbative QCD Approach

Abstract

In this paper, we calculate the branching ratios and CP-violating asymmetries for $B_{s} \to (ρ^0,ω, ϕ) η^{(\prime)}$ decays in the perturbative QCD (pQCD) factorization approach. Numerically we found that (a) the pQCD predictions for the CP-averaged branching ratios are $Br(B_{s}\toρ^0 η)\approx 0.07 \times 10^{-6}$, $Br(B_{s}\toρ^{0}η^\prime) \approx 0.10 \times 10^{-6}$, $Br(B_{s} \toωη) \approx 0.02 \times 10^{-6}$, $Br(B_{s} \toωη^\prime) \approx 0.13 \times 10^{-6}$, $Br(B_{s} \toϕη) \approx 2.7 \times 10^{-5}$ and $Br(B_{s} \toϕη^\prime) \approx 2.0 \times 10^{-5}$; (b) the gluonic contributions are small in size: less than 3% for $B \to (ρ, ω, ϕ) η$ decays, and about 10% for $B \to (ρ, ω, ϕ) η^\prime$ 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.