Production of high $p_{T}$ $J/\psi$ in p+p collisions at $\sqrt{s_{NN}}=200$ GeV in STAR

Suppression of the $J/\psi$ production by color screening in ultra-relativistic heavy-ion collisions was suggested as the signature of the Quark-Gluon Plasma formation. Measurement of $J/\psi$ production in p+p collisions is a baseline measurement which allows to verify the $J/\psi$ suppression in A+A collisions and could provide information about the $J/\psi$ production mechanism. Run 2008 p+p STAR data was taken with reduced detector material, therefore it has significantly reduced background compare to the earlier runs. In this presentation, the preliminary analysis of mid-rapidity $J/\psi$ production at high transverse momentum through dielectron decay channel in p+p collisions at $\sqrt{s_{NN}}=200$ GeV from year 2008 will be shown.