$B_s\to (\rho ,\omega ,\varphi ){\eta }^{(\prime )}$ Decays in the Perturbative QCD Approach

Abstract

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

Comments: 24 pages, 8 ps and eps figures, Revtex