$\psi$(2S) production in Pb-Pb collisions measured by ALICE at the LHC

Charmonium production is a probe sensitive to deconfinement in nucleus-nucleus collisions. The production of J/$\psi$ via regeneration within the QGP or at the phase boundary has been identified as an important ingredient for the description of the observed J/$\psi$ nuclear modification factor at the LHC. The $\psi(2S)$ production relative to J/$\psi$ is a possible discriminator between the two regeneration scenarios. Studies of $\psi(2S)$ production in central nucleus-nucleus collisions at low transverse momentum ($p_{\rm T}$) are crucial, particularly at the LHC, where regeneration appears to be dominant. A significant $\psi$(2S) signal is extracted at low $p_{\rm T}$ and forward rapidity in the dimuon decay channel for the first time. This measurement relies on the $\psi(2S)$ cross section measured recently in pp collisions at $\sqrt{s_{\rm }}=5.02$ TeV with an unprecedented precision compared to previous ALICE results. In this contribution, we present newly published results on the $\psi(2S)$-to-J/$\psi$ ratio and the $\psi(2S)$ nuclear modification factor in Pb-Pb collisions at $\sqrt{s_{\rm NN}}=5.02$ TeV. Results are reported as a function of centrality and $p_{\rm T}$ for $p_{\rm T}<12$ GeV/c and are compared to available NA50 and CMS measurements. Comparisons to transport and statistical hadronization model predictions are also provided to shed light on the charmonium states recombination mechanism