Energy dependence of $J/\psi$ production in p+p collisions at STAR

$J/\psi$ production in heavy-ion collisions is an important tool for studying the properties of Quark-Gluon Plasma (QGP). Interpretation of these results requires a good understanding of the production mechanisms in p+p collisions, which include direct production via gluon fusion, parton fragmentation, and feed down from excited charmonium states and B hadrons. Despite decades of efforts, the $J/\psi$ production mechanism still remains a puzzle in high energy physics. $J/\psi$ measurement at a new beam energy provides new insights on $J/\psi$ production mechanism and constrains theoretical parameters. In 2013, a large fraction of the Muon Telescope Detector (MTD) was installed at mid-rapidity in STAR. This enables, for the first time, the measurement of $J/\psi$ at STAR via the di-muon channel. In this talk, we will present the measurement on $J/\psi$ production in p+p collisions at $\sqrt{s} = 200$ and 500 GeV in a wide $p_{T}$ range up to 20 GeV/c, by combing measurements from the MTD and the other detectors. We will discuss the physics perspectives of $J/\psi$ measurement in the forward pseudo-rapidity range $2.5 < \eta < 4.5$ with the proposed future Forward Calorimeter System and Forward Tracking System at STAR.