Hadronic scattering effects on $\psi(2S)$ suppression in relativistic heavy-ion collisions

In this work we estimate the $N_{\psi(2S)} / N_{J/\psi}$ yield ratio in heavy-ion collisions, considering the interactions of the $\psi (2S) $ and $J/\psi$ states with light mesons in the hadron gas formed at the late stages of these collisions. Starting from the appropriate effective Lagrangians, we first compute the thermally-averaged cross sections for the production and absorption of the mentioned states, and then use them as input in the rate equations to determine the time evolution of $N_{\psi(2S)}$, $N_{J/\psi}$ and $N_{\psi(2S)} / N_{J/\psi}$. The main conclusion of our study is that the $\psi (2S) $ and $J/\psi$ multiplicities do not change much in the hadron gas phase and that the $\psi (2S)$ is more absorbed than the $J/\psi$. The obtained final ratio is in qualitative agreement with experimental data.