$B_s\to PP$ decays and the NLO contributions in the pQCD Approach

By employing the perturbative QCD(pQCD) factorization approach, we calculated the partial next-to-leading order (NLO) contributions to $B_s\to PP$ decays ($P=\pi ,K,\text{etap}$), coming from the QCD vertex corrections, the quark-loops and the chromo-magnetic penguins. we found numerically that (a) for three measured decays ${\bar{B}}_s\to K^{+}{\pi }^{-},K^{+}{K}^{-}$ and ${\pi }^{+}{\pi }^{-}$, the consistency between the pQCD predictions and the measured values are improved effectively by the inclusion of the NLO contributions; (b) for $\bar{B}_s \to K^0\etap$and$K^0\pi^0$ decays, the NLO enhancements to the branching ratios can be significant, from $\sim 50$ to 170%, to be tested by the LHC experiments; © for the CP-violating asymmetries, the leading order pQCD predictions can also be changed significantly by the inclusion of the NLO contributions; (d) for ${\bar{B}}_s\to K^{+}{\pi }^{-}$ decay, the pQCD prediction for the direct CP asymmetry is ${\text{acp}}^{dir}({\bar{B}}_s\to K^{+}{\pi }^{-})=0.26\pm 0.06$, which agrees very well with the only measured value available currently.