$B_{s} \to PP $ decays and the NLO contributions in the pQCD Approach

Abstract

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