It is expected that the charmonium state $J/ \psi$ produced during the hadronization of the quark-gluon plasma suffers a rescattering process between the chemical freeze-out and the kinetical freeze-out. We present an updated study of the suppression and generation of the $J/\psi$ meson due to its interaction with a hadronic medium composed of light pseudo-scalar (as $\pi, K, \eta$) and vector mesons (as $\rho, K^*, \omega$). The absorption (production) cross-sections are obtained considering s-wave processes with the channels $J/\psi + (\pi,\rho,K,K^*,\eta,\omega) $ in initial (final) state.
The meson-meson interactions are described using a chiral unitary approach with a $SU(4)$ effective Lagrangian. The symmetry is explicitly broken to $SU(3)$ by suppression of the interactions driven by charmed mesons.