Transverse Single Spin Asymmetries in \textit{J/$\psi $} Production in Polarized p+p Collisions at $\sqrt s $=200 GeV, measured in the PHENIX Detector at RHIC

The measurement of transverse single spin asymmetries ($A_{N})$ gives us an opportunity to probe the quark and gluon structure of transversely polarized nucleons. At RHIC energies, heavy flavor production is dominated by gluon-gluon fusion. Because the gluon transversity is zero, The Collins effect has minimal impact on $A_{N}$ in heavy flavor production. The measurement of $A_{N}$ in heavy flavor production is uniquely sensitive to the gluon Sivers effect which is potentially related to the orbital angular momentum of gluons inside the polarized protons. The latest measurement of transverse SSAs in \textit{J/$\psi $} production is presented. The data were taken by the PHENIX experiment at the Relativistic Heavy Ion Collider (RHIC) during the 2006 and 2008 run in transverse polarized proton+proton collisions at $\sqrt s $=200 GeV. The $p_{T}$ and $x_{F}$ dependencies are studied in rapidity regions -2.2 $<$ y $<$ -1.2, $\vert $y$\vert \quad <$ 0.35, and 1.2 $<$ y $<$ 2.2, and $p_{T}$ up to 6 GeV/c.