Rare Higgs Decays into $J/\psi$ Mesons*

Rare decays of the Higgs boson to $J/\psi$ mesons are a promising laboratory to study couplings to charm quarks and physics beyond the standard model. A search for decays of the Higgs boson to $J/\psi$ meson pairs and $Z$ boson plus $J/\psi$ meson, with the subsequent resonance decays to muon pairs is performed with the Compact Muon Solenoid detector at the Large Hadron Collider. A data sample of proton-proton collisions collected at a center-of-mass energy of 13 TeV during the years 2016, 2017 and 2018 is used. I will present results of the searches and implications for future searches of beyond standard model signatures at high luminosity.