Exclusive charmless $B_s$ hadronic decays into ${\eta }^{\prime }$ and $\eta$

Abstract

Using the next-to-leading order QCD-corrected effective Hamiltonian, charmless exclusive nonleptonic decays of the $B_s$ meson into $\eta$ or ${\eta }^{\prime }$ are calculated within the generalized factorization approach. Nonfactorizable contributions, which can be parametrized in terms of the effective number of colors $N_c^{\mathrm{eff}}$ for $PP$ and $VP$ decay modes, are studied in two different schemes: (i) the one with the "homogeneous" structure in which $(N_c^{\mathrm{eff}}{)}_1\approx (N_c^{\mathrm{eff}}{)}_2\approx ...\approx (N_c^{\mathrm{eff}}{)}_{10}$ is assumed, and (ii) the "heterogeneous" one in which the possibility of $N_c^{\mathrm{eff}}(V+A)\ne N_c^{\mathrm{eff}}(V-A)$ is considered, where $N_c^{\mathrm{eff}}(V+A)$ denotes the effective value of colors for the $(V-A)(V+A)$ penguin operators and $N_c^{\mathrm{eff}}(V-A)$ for the $(V-A)(V-A)$ ones. For processes depending on the $N_c^{\mathrm{eff}}$-stable $a_i$ such as $\overline{B_s}\to (\pi ,\rho )({\eta }^{{}^{\prime }},\eta )$, the predicted branching ratios are not sensitive to the factorization approach we choose. While for the processes depending on the $N_c^{\mathrm{eff}}$-sensitive $a_i$ such as $\overline{B_s}\to \omega {\eta }^{{(}^{\prime })}$, there is a wide range for the branching ratios depending on the choice of the $N_c^{\mathrm{eff}}$ involved. We have included the QCD anomaly effect in our calculations and found that it is important for $\overline{B_s}\to {\eta }^{{(}^{\prime })}{\eta }^{{(}^{\prime })}$. The effect of the $(c\bar{c})\to {\eta }^{\prime }$ mechanism is found to be tiny due to a possible CKM-suppression and the suppression in the decay constants except for the $\overline{B_s}\to \varphi \eta$ decay within the "naive" factorization approach, where the internal $W$ diagram is CKM-suppressed and the penguin contributions are compensated.

13 pages

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Cited by in corpus (11)

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• Estimating Form Factors of $B_s\to D_s^{(\ast )}$ and their Applications to Semi-leptonic and Non-leptonic Decays
• Charmless ${\bar{B}}_s\to VV$ Decays in QCD Factorization
• Connecting $b\to s\ell \bar{\ell }$ anomalies to enhanced rare nonleptonic ${\bar{B}}_s^0$ decays in $Z^{\prime }$ model
• Branching Ratio and CP Asymmetry of $B_s\to \rho (\omega )K$ Decays in the Perturbative QCD Approach
• Branching ratios and CP-violating asymmetries of $B_s\to h_1{h}_2$ decays in the general two-Higgs doublet models
• Branching Ratio and CP Asymmetry of $B_s\to {\pi }^0{\eta }^{(\prime )}$ Decays in the perturbative QCD Approach
• Charmless $B_s\to PP,PV,VV$ Decays Based on the six-quark Effective Hamiltonian with Strong Phase Effects II
• Rare nonleptonic ${\bar{B}}_s^0$ decays as probes of new physics behind $b\to s\mu \bar{\mu }$ anomalies