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By employing the perturbative QCD (PQCD) factorization approach, we made asystematic investigation for the CP-averaged branching ratios and theCP-violating asymmetries of the thirteen $\bar{B}^0_s \to PP $ decays ( here$P=(\pi,K, \eta, \eta^{\prime})$) with the inclusion of all currently knownnext-to-leading order (NLO) contributions, and compared our results with themeasured values or the theoretical predictions from other different approaches.We focused on the examination of the effects of the NLO contributions and foundthe following points: (a) for $\bar{B}_s^0 \to (K^0 \bar{K}^0, K^+ K^-,\eta^\prime \eta^\prime,\pi^- K^+)$ decays, the NLO contributions can provide a$(40-150) \%$ enhancement or a $20\%$ reduction to the corresponding leadingorder (LO) PQCD predictions for their decay rates and result in a much betteragreement between the PQCD predictions and the experimental measurements; (b)for the pure annihilation decay $\bar{B}_s^0 \to \pi^+\pi^-$, the PQCDprediction still remain consistent with the data after the inclusion of thesmall NLO reduction; (c) the PQCD predictions for the ratio $(f_s/f_d)\cdot{\cal B}(B_s^0\to \pi^+\pi^-)/{\cal B}(B^0\to K^+\pi^-)$ and $(f_s/f_d)\cdot{\cal B}(B_s^0\to \pi^+ K^-)/{\cal B}(B^0\to K^+\pi^-)$ become agree very wellwith the measured ones after the inclusion of a $40\%$ NLO reduction; (d) for$\bar{B}_s^0 \to K^+ K^-$ and $\bar{B}_s^0 \to \pi^- K^+$ decays, the NLO PQCDpredictions for their CP-violating asymmetries do agree very well with themeasured values in both the sign and the magnitude; and (e) for all$\bar{B}_s^0 \to P P$ decays, we also compared our results with those obtainedin the QCD factorization approach and soft-collinear effective theory anddiscussed their similarities and differences.

Anatomy of $B_s \to PP $ decays and effects of the next-to-leading order contributions in the perturbative QCD approach