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

TL;DR

This paper calculates branching ratios and CP asymmetries for specific $ar{B}_s^0$ decays using pQCD, highlighting the significant impact of next-to-leading order contributions on predictions and their potential measurability in experiments.

Contribution

It provides the first comprehensive analysis of NLO effects on these decay modes within the pQCD framework, improving the accuracy of theoretical predictions.

Findings

NLO contributions double the decay rates for some modes.

NLO effects significantly enhance direct CP asymmetries.

Predicted branching ratios are within experimental detection range.

Abstract

In this paper, we calculate the branching ratios and CP violating asymmetries of the five $\bar{B}^0_s \to (\pi^0\eta^{(*)},\eta^{(*)}\eta^{(*)})$ 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 $Br(\bar{B}_s \to \pi^0 \eta^{(*)})$ 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 $\bar{B}_s \to \pi^0 \eta^{(*)}$ 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 $Br(\bar{B}_s \to \eta \eta^{(*)})$ 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.