Elliptic and triangular flow of charmonium states in heavy ion collisions

We study the elliptic and triangular flow of charmonium states, or $J/\psi$, $\psi(2S)$, and $\chi_c(1P)$ mesons in heavy ion collisions. Starting from the evaluation of charmonia transverse momentum distributions and yields, we calculate elliptic and triangular flow of charmonium states based on the coalescence model. We show that the internal structure, or the wave function distribution of charmonium states plays a significant role, especially when charmonium states are produced by charm quark recombination, leading to the transverse momentum distribution of the $\psi(2S)$ meson as half large as that of the $J/\psi$ meson. We also consider the dependence of the elliptic and triangular flow of charmonium states on internal structures of charmonium states, and find that the wave function effects as well as feed-down contributions are averaged out for elliptic and triangular flow, resulting in similar elliptic and triangular flow for all charmonium states. We investigate further the elliptic and triangular flow of charmonium states at low transverse momentum region, and also discuss the quark number scaling of elliptic and triangular flow for charmonium states.