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

Abstract

In this paper, we calculate the branching ratios and CP violating asymmetries of the five ${\bar{B}}_s^0\to ({\pi }^0{\eta }^{(\ast )},{\eta }^{(\ast )}{\eta }^{(\ast )})$ decays, by employing the perturbative QCD (pQCD) factorization approach and with the inclusion of all currently known next-to-leading order (NLO) contributions. We find that (a) the NLO contributions can provide about 100% enhancements to the LO 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 $Br({\bar{B}}_s\to {\pi }^0{\eta }^{(\ast )})$ and $Br({\bar{B}}_s\to \eta \eta )$; (b) the newly known NLO twist-2 and twist-3 contributions to the relevant form factors can provide about 10% enhancements to the decay rates of the considered decays; (c) for ${\bar{B}}_s\to {\pi }^0{\eta }^{(\ast )}$ decays, their direct CP-violating asymmetries $\cala_f^{dir}$ could be enhanced significantly by the inclusion of the NLO contributions; and (d) the pQCD predictions for $Br({\bar{B}}_s\to \eta {\eta }^{(\ast )})$ 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-B experiments.

arXiv comment12 pages, 2figures and 3 tables

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• Anatomy of $B_s\to PV$ decays and effects of next-to-leading order contributions in the perturbative QCD factorization approach
• Radiative $h_{c/b}$ decays to $\eta$ or ${\eta }^{\prime }$
• Anatomy of $B_s\to PP$ decays and effects of the next-to-leading order contributions in the perturbative QCD approach
• Form factors for semileptonic $B_c$ decays into ${\eta }^{{(}^{\prime })}$ and Glueball