  Rare Higgs decays into a pair of heavy vector quarkonia, $h\to VV$
($V=J/\Psi$, $\Upsilon$ etc.), have been investigated in the standard model.
Different from the past literature in which these decays are thought to be only
dominated by the longitudinally polarized final states, we also include the
transitions, which proceed through $h\to \gamma^*\gamma^*$/$h\to V\gamma^*$,
followed by $\gamma^*\to V$. The final vector quarkonia via these ways are
dominantly transversely polarized. Our calculation however shows that these
transitions could lead to significant contributions to the decay rate,
especially for the charmonium final states. The total branching ratios of these
processes are predicted to be around $10^{-10}$, far below the current
experimental upper bounds. Hopefully, experimental studies of these very rare
decays in future high-precision experimental facilities might be interesting
both to test the standard model and to look for new physics scenarios.
