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

TL;DR

This paper calculates next-to-leading order contributions to $B_s o P P$ decays using pQCD, improving predictions for branching ratios and CP asymmetries, and providing results consistent with current measurements and testable predictions for future experiments.

Contribution

It provides the first detailed NLO pQCD calculations for $B_s o P P$ decays, enhancing the accuracy of theoretical predictions and aligning them more closely with experimental data.

Findings

NLO contributions improve agreement with measured decay rates.

Significant NLO enhancements predicted for certain decay modes.

CP asymmetry predictions are notably affected by NLO corrections.

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= \pi, 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 $\bar{B}_s \to K^+ \pi^-, K^+K^-$ 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; (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 $\bar{B}_s \to K^+\pi^-$ decay, the pQCD prediction for the direct CP asymmetry is $\acp^{dir}(\bar{B}_s \to K^+\pi^-)=0.26\pm 0.06$, which agrees very well with the only measured value available currently.