Psi(2S) Production at the LHC

We calculate the production of $\psi(2S)$ and the pertinent double ratio of its nuclear modification factor ($R_{\rm AA}$) over that of the $J/\psi$ in Pb-Pb collisions at the LHC. Based on a transport model with temperature dependent reaction rates, a sequential regeneration pattern emerges: the larger $\psi(2S)$ width, relative to the $J/\psi$, around and below the critical temperature, implies that most of the $\psi(2S)$ states are regenerated later in the evolution of the fireball. This has noticeable consequences for the transverse-momentum ($p_T$) spectra of the regenerated charmonia. While the total yield of $\psi(2S)$ meson remains smaller than those of $J/\psi$'s, their harder $p_T$ spectra can produce a double ratio above unity for a $p_T>3$GeV cut, as applied by the CMS collaboration. A significant uncertainty in our calculations is associated with the values of the temperature where most of the $\psi(2S)$ regeneration occurs, the quantitative temperature dependence of its inelastic width.