Measurements of charmonium production in p$+$p, p$+$Au, and Au$+$Au collisions at $\sqrt{s_{_{\rm NN}}}$~=~200~GeV with the STAR experiment

Abstract: We present the first results from the STAR MTD of mid-rapidity charmonium measurements via the di-muon decay channel in p$+$p, p$+$Au, and Au$+$Au collisions at $\sqrt{s_{_{\rm NN}}}=200$~GeV at RHIC. The inclusive $J/\psi$ production cross section in p$+$p collisions can be described by the Non-Relativistic QCD (NRQCD) formalism coupled with the color glass condensate effective theory (CGC) at low transverse momentum ($p_T$) and next-to-leading order NRQCD at high $p_T$. The nuclear modification factor in p$+$Au collisions for inclusive $J/\psi$ is below unity at low $p_T$ and consistent with unity at high $p_T$, which can be described by calculations including both nuclear PDF and nuclear absorption effects. The double ratio of inclusive $J/\psi$ and $\psi(2S)$ production rates for $0<p_T<10$~GeV/$c$ at mid-rapidity between p$+$p and p$+$Au collisions is measured to be 1.37~$\pm$~0.42~$\pm$~0.19. The nuclear modification factor in Au$+$Au collisions for inclusive $J/\psi$ shows significant $J/\psi$ suppression at high $p_T$ in central collisions and can be qualitatively described by transport models including dissociation and regeneration contributions.