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Semileptonic decays $B/B_s \to (η,\etar, G)(l^+l^-,l\barν,ν\barν)$ in the perturbative QCD approach beyond the leading order

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