Study of $J/\psi$ production with jet activity in $pp$ collisions at $\sqrt{s}$ = 200 GeV at the STAR experiment

The fragmentation function is believed to play a crucial role to differentiate different production mechanisms of $J/\psi$. In order to have a better understanding of charm quarks and gluons fragmenting into $J/\psi$, production of $J/\psi$ mesons in jets has been studied in $pp$ collisions at the LHC and RHIC. The measured $J/\psi$ production is found to be much less isolated than nonrelativistic QCD (NRQCD) prediction as implemented in PYTHIA. The dependence of $J/\psi$ production on jet activity (the number of jets per event) is another observable which could be easily compared with theoretical predictions to understand the relation between jet fragmentation and $J/\psi$ production. In this talk, we will present the progress of the study of $J/\psi$ production with jet activity at mid-rapidity in $pp$ collisions at $\sqrt{s}$ = 200 GeV at the STAR experiment.