$B_s^0\to {\eta }^{(\prime )}{\eta }^{(\prime )}$ decays in the pQCD approach

Abstract

We calculate the CP averaged branching ratios and CP-violating asymmetries for $B_s^0\to \eta \eta ,\eta {\eta }^{\prime }$ and ${\eta }^{\prime }{\eta }^{\prime }$ decays in the perturbative QCD (pQCD) approach here. The pQCD predictions for the CP-averaged branching ratios are Br(B_s^0 \to \eta \eta) = \left (14.2^{+18.0}_{-7.5}) \times 10^{-6}, Br(B_s^0 \to \eta \eta^\prime)= \left (12.4 ^{+18.2}_{-7.0}) \times 10^{-6}, and Br(B_s^0 \to \eta^{\prime} \eta^{\prime}) = \left (9.2^{+15.3}_{-4.9}) \times 10^{-6}, which agree well with those obtained by employing the QCD factorization approach and also be consistent with available experimental upper limits. The gluonic contributions are small in size: less than 7% for $B_s\to \eta \eta$ and $\eta {\eta }^{\prime }$ decays, and around 18% for $B_s\to {\eta }^{\prime }{\eta }^{\prime }$ decay. The CP-violating asymmetries for three decays are very small: less than 3% in magnitude.

Comments: 11 pages, 1 ps figure, Revtex