Study of event multiplicity and $J/\psi$ production in p+p and p+Au collisions at PHENIX experiment

$J/\psi$ production has been studied extensively in heavy ion collisions at RHIC and other facilities for decades. However, there are still large uncertainties in our understanding of the production mechanisms, and various contributions from the initial and final state effects quantitatively. To gain additional information that could help us to further constrain these uncertainties, we study the impacts of the event multiplicity on the J/ψ production. Specifically, we study the $J/\psi$ yields at the forward and backward rapidities (1.2<|y|<2.2) in 200 GeV p+p and p+Au collisions recorded by the PHENIX experiment at RHIC in the 2015 data taking period, as a function of the event charged track multiplicity in the forward, central, and backward rapidities. The latest status of this study will be presented.