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Higgs boson decay to charmonia via $c$-quark fragmentation

We calculate the decay branching fractions of the Higgs boson to $J/ψ$ and $η_c$ via the charm-quark fragmentation mechanism for the color-singlet and color-octet states in the framework of non-relativistic QCD. The decay rates are governed by the charm-quark Yukawa coupling, unlike the decay $H\to J/ψ+ γ$, which is dominated by the $γ^*$-$J/ψ$ mixing. We find that the decay branching fractions can be about $2 \times 10^{-5}$ for $H\to c{\bar c}+J/ψ$, and $6 \times 10^{-5}$ for $H\to c{\bar c}+η_c$. We comment on the perspective of searching for the Higgs boson to $J/ψ$ transition at the High-Luminosity LHC for testing the charm-quark Yukawa coupling.