Enhanced production of $\psi (2S)$ mesons in heavy ion collisions

We study the production of a $\psi (2S)$ meson in heavy ion collisions. We evaluate Wigner functions for the $\psi (2S)$ meson using both Gaussian and Coulomb wave functions, and investigate the wave function dependence in the $\psi (2S)$ meson production by recombination of charm and anti-charm quarks. The enhanced transverse momentum distribution of $\psi (2S)$ mesons compared to that of $J\mathrm{/}\psi$ mesons, originated from wave function distributions of the $\psi (2S)$ and $J\mathrm{/}\psi$ meson in momentum space, provides a plausible explanation for the recent measurement of the nuclear modification factor ratio between the $\psi (2S)$ and $J\mathrm{/}\psi$ meson.