Non-perturbative QCD effects in ${\eta }_c$ and ${\eta }_b$ decays into baryons and WIMP scattering off nuclei

In this work we estimate the helicity suppressed decay rates of ${\eta }_b$ resonances into baryon pairs due to instanton-induced effects by rescaling the corresponding partial widths of the experimentally measured branching ratios for the ${\eta }_c(1S)\to p\bar{p}$ and ${\eta }_c(1S)\to \mathrm{\Lambda }\overline{(}\mathrm{\Lambda })$ decay modes. Thus we point out that both ${\eta }_b(1S)\to p\bar{p}$ and ${\eta }_b(1S)\to \mathrm{\Lambda }\overline{(}\mathrm{\Lambda })$ 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.