A note on Higgs decays into $Z$ boson and $J/Ψ(Υ)$

Rare decays $h\to Z V$ with $V$ denoting the narrow $c\bar{c}$ or $b\bar{b}$ resonances, such as $J/Ψ$ or $Υ$ states, have been analyzed. Within the standard model, these channels may proceed through the tree-level transition $h\to ZZ^*$ with the virtual $Z^*\to V$, and also loop-induced process $h\to Zγ^*$, followed by $γ^*\to V$. Our analysis shows that, for the bottomonium final states, the decay rate of $h\to Z Υ$ from the loop-induced process is small and the former transition gives the dominant contribution; while, for the charmonium final states, $Γ(h\to Z J/Ψ)$ and $Γ(h\to ZΨ(2S))$ induced by $h\to Zγ^* \to Z V$ could be comparable to the contribution given by the tree-level $h\to ZZ^*\to Z V$ transition.

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