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In this paper, we calculate the branching ratios and CP violating asymmetriesof the five $\bar{B}^0_s \to (\pi^0\eta^{(*)},\eta^{(*)}\eta^{(*)})$ decays, byemploying the perturbative QCD (pQCD) factorization approach and with theinclusion of all currently known next-to-leading order (NLO) contributions. Wefind that (a) the NLO contributions can provide about 100% enhancements to theLO pQCD predictions for the decay rates of $\bar{B}_s^0 \to \eta\eta^\prime$and $\eta^\prime \eta^\prime$ decays, but result in small changes to$Br(\bar{B}_s \to \pi^0 \eta^{(*)})$ and $Br(\bar{B}_s \to \eta\eta)$; (b) thenewly known NLO twist-2 and twist-3 contributions to the relevant form factorscan provide about 10% enhancements to the decay rates of the considered decays;(c) for $\bar{B}_s \to \pi^0 \eta^{(*)}$ decays, their direct CP-violatingasymmetries $\cala_f^{dir}$ could be enhanced significantly by the inclusion ofthe NLO contributions; and (d) the pQCD predictions for $Br(\bar{B}_s \to \eta\eta^{(*)})$ and $Br(\bar{B}_s \to \eta^\prime \eta^\prime)$ can be as large as$4\times 10^{-5}$, which may be measurable at LHCb or the forthcoming super-Bexperiments.

physical review. d. particles, fields, gravitation, and cosmology/physical review. d, particles, fields, gravitation, and cosmology

$\bar{B}^0_s \to (\pi^0 \eta^{(*)}, \eta^{(*)}\eta^{(*)})$ decays and  the effects of next-to-leading order contributions in the perturbative QCD  approach