In this paper we make a systematic study of the semileptonic decays $B/B_s\to (\eta ,{\eta }^{\prime },G)(l^{+}{l}^{-},l\overline{\nu },\nu \overline{\nu })$ by employing the perturbative QCD (pQCD) factorization approach. The next-to-leading-order (NLO) contributions to the relevant form factors are included, and the ordinary $\eta \mathrm{\text{−}}{\eta }^{\prime }$ mixing scheme and the $\eta \mathrm{\text{−}}{\eta }^{\prime }\mathrm{\text{−}}G$ mixing scheme are considered separately, where $G$ denotes a pseudoscalar glueball. The numerical results and the phenomenological analysis indicate that (a) the NLO contributions to the relevant form factors provide 25% enhancement to the leading-order pQCD predictions for the branching ratios $\mathrm{Br}(B^{-}\to {\eta }^{{(}^{\prime })}{l}^{-}{\overline{\nu }}_l)$, leading to a good agreement between the predictions and the data; (b) for all considered decays, the pQCD results are basically consistent with those from other different theoretical models; (c) the pQCD predictions in the two considered mixing schemes agree well with each other within theoretical errors. The outcomes presented here can be tested by LHCb and forthcoming Super-$B$ experiments.

• Received 2 January 2013

DOI:https://doi.org/10.1103/PhysRevD.87.097501