Study of $J/\psi$ production at low $p_T$ in Cu+Cu collisions at $\sqrt{s_{NN}}=200$ GeV at STAR experiment

$J/\psi$ production in Cu+Cu collisions at $\sqrt{s_{NN}}=200$ GeV has been measured by STAR experiment at RHIC. Cu+Cu is particularly interesting because it is positioned between d+Au where only cold nuclear matter effects are present and Au+Au where significant suppression due to hot nuclear matter was reported. In this talk the study of $J/\psi$ production at low $p_T$ in Cu+Cu at $\sqrt{s_{NN}}=200$ GeV will be reported. The $J/\psi$ invariant yield and nuclear modification factor as a function of transverse momentum (up to 5 GeV/c) and centrality will be presented. The results of $J/\psi$ in Cu+Cu will be compared to relevant p+p data, PHENIX Cu+Cu measurement and various theoretical models.