  In this paper we make a systematic study of the semileptonic decays $B/B_s
\to (\eta,\etar, G)(l^+l^-,l\bar{\nu},\nu\bar{\nu})$ 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
$\eta$-$\etar$ mixing scheme and the $\eta$-$\etar$-$G$ 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 $Br(B^-\to \eta^{(')}
l^-\bar{\nu}_l)$, 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.
