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 \title{System size and collision energy dependences of $J/\psi$ production at RHIC from the STAR experiment}
 \author{Qian Yang, Ziyue Zhang, Yu-Ming Liu, Yan Wang and Kaifeng Shen}
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 \begin{abstract}\large
Charm quarks are an important probe to study the properties of the quark-gluon plasma (QGP) created in heavy-ion collisions. 
The $J/\psi$ anisotropy flow, $v_{2}$, gives information about the charm quark thermalization and $J/\psi$ regeneration effect.
On the other hand, $J/\psi$ nuclear modification factor in p+Au collisions, $R_{pA}$, can be used to probe cold nuclear matter effects, while in Au+Au collisions $R_{AA}$ is sensitive to the hot nuclear matter effect in QGP. Measurements of $J/\psi$ $v_{2}$ and $R_{AA}$ in different collision systems and energies can help to better understand the $J/\psi$ production and  the QGP properties.
The STAR isobar program (Ru+Ru and Zr+Zr collisions at $\sqrt{s_{NN}} = 200$ GeV) provides a unique opportunity to study the $J/\psi$ regeneration and dissociation contributions in a modest size system between p+Au and central Au+Au system. 
 
In this talk, the $J/\psi$ $v_{2}$ as a function of transverse momentum and centrality using high statistics isobar collision data will be shown. Additionally, the $J/\psi$ nuclear modification factors will be presented in p+Au, Ru+Ru and Zr+Zr at  $\sqrt{s_{NN}} = 200$ GeV as well as in Au+Au  $\sqrt{s_{NN}} = 54.4$ GeV.

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