$J/\psi$ production in minimum bias Au+Au and Cu+Cu collisions at $\sqrt{s_{NN}}=200$ GeV at STAR

$J/\psi$ production is considered to be a sensitive probe of the properties of quark gluon plasma created in nucleus+nucleus collisions at RHIC. It has been studied in Au+Au and Cu+Cu collisions in the last years, and new Au+Au data taken by the STAR detector in year 2007 has recently become available, significantly improving statistics. In this presentation, the analysis of mid-rapidity($\left|y \right| < 1$) $J/\psi$ production via the dielectron decay channel in Au+Au(year 2007) and Cu+Cu(year 2005) collisions at $\sqrt{s_{NN}}=200$ GeV at STAR is reported. It is compared to STAR p+p results in order to study the nuclear modification factor as a function of transverse momentum and centrality. The results are compared to previously published data and available theoretical models.