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A bstract 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 → J / ψ + γ , which is dominated by the γ ∗ - J / ψ mixing. We find that the decay branching fractions can be about 2 × 10 − 5 for $$ H\to c\overline{c}+J/\psi $$ H → c c ¯ + J / ψ , and 6 × 10 − 5 for $$ H\to c\overline{c}+{\eta}_c $$ H → c 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. 

In this paper, we study the fragmentation of a heavy quark into a jet near threshold, meaning that final state jet carries most of the energy of the fragmenting heavy quark. Using the heavy quark fragmentation function, we simultaneously resum large logarithms of the jet radius R and 1 − z, where z is the ratio of the jet energy to the initiating heavy quark energy. There are numerically significant corrections to the leading order rate due to this resummation. We also investigate the heavy quark fragmentation to a groomed jet, using the soft drop grooming algorithm as an example. In order to do so, we introduce a collinear-ultrasoft mode sensitive to the grooming region determined by the algorithm’s zcut parameter. This allows us to resum large logarithms of zcut/(1−z), again leading to large numerical corrections near the endpoint. A nice feature of the analysis of the heavy quark fragmenting to a groomed jet is the heavy quark mass m renders the algorithm infrared finite, allowing a perturbative calculation. We analyze this for EJ R ∼ m and EJ R ≫ m, where EJ is the jet energy. To do the latter case, we introduce an ultracollinear-soft mode, allowing us to resum large logarithms of EJ R/m. Finally, as an application we calculate the rate for e+e− collisions to produce a heavy quark jet in the endpoint region, where we show that grooming effects have a sizable contribution near the endpoint.