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Non-perturbative QCD effects in $η_c$ and $η_b$ decays into baryons and WIMP scattering off nuclei

In this work we estimate the helicity suppressed decay rates of $η_b$ resonances into baryon pairs due to instanton-induced effects by rescaling the corresponding partial widths of the experimentally measured branching ratios for the $η_c(1S) \to p\bar{p}$ and $η_c(1S) \to Λ\bar(Λ)$ decay modes. Thus we point out that both $η_b(1S) \to p\bar{p}$ and $η_b(1S) \to Λ\bar(Λ)$ channels could be detected at a Super B factory and LHC experiments. Furthermore, we examine related instanton-induced effects on WIMP scattering off nuclei concluding, albeit with large uncertainties, that they might enhance the spin-dependent cross section for a light pseudoscalar Higgs boson mediator, thereby inducing a dependence on the momentum transfer to the recoling nucleus.