Survival of charmonia in a hot environment

A colorless $\overline{c}c$ dipole emerging from a heavy ion collision and developing the charmonium wave function can be broken up by final state interactions (FSI) propagating through the hot medium created in the collision. We single out two mechanisms of charmonium attenuation: (i) Debye color screening, called melting; and (ii) color-exchange interaction with the medium, called absorption. The former problem was treated so far only for charmonia at rest embedded in the medium, while in practice their transverse momenta at the LHC are quite high, $\langle p_T^2\rangle =7$–10 ${\mathrm{GeV}}^2$. We demonstrate that a $\overline{c}c$ dipole may have a large survival probability even at infinitely high temperature. We develop a procedure of Lorentz boosting of the Schrödinger equation to a moving reference frame and perform the first realistic calculations of the charmonium survival probability employing the path-integral technique, incorporating both melting and absorption. These effects are found to have comparable magnitudes. We also calculated the FSI suppression factor for the radial excitation $\psi \left(2S\right)$ and found it to be stronger than for $J/\psi$, except large $p_T$, where $\psi \left(2S\right)$ is relatively enhanced. The azimuthal asymmetry parameter $v_2$ is also calculated.

Figure 1

The attenuation factor ${\left|S\left(L\right)\right|}^2$ for $J/\psi$ produced with momentum $p_{\psi }\equiv p_T$ off a hot medium. The Debye screening in the medium is assumed to have maximal magnitude completely eliminating the $\overline{c}c$ binding potential during in-medium propagation over the path length $L$.

Figure 2

Kinematic variables for the Bethe-Salpeter bound state diagram.

Figure 3

The FSI suppression factor calculated with Eq. (28) for $J/\psi$ produced with momentum $p_{\psi }\equiv p_T$ in central lead-lead collisions. The absorption effects are eliminated by fixing $\mathrm{Im}U=0$, to single out the net effect of Debye screening. The curves from top to bottom are calculated with $q_0=0.5,1,2$, and $4{\text{GeV}}^2/\text{fm}$.

Figure 4

Same as in Fig. 3, but with the net effect of absorption, i.e., with eliminated Debye screening.

Figure 5

Same as in Figs. 3 and 4, but including both screening and absorption effects.

Figure 6

The curves from top to bottom show the attenuation factor ${\left|S\left(L\right)\right|}^2$ vs $J/\psi$ momentum for either pure absorption, or pure melting, and for both effects included, respectively. The calculations are performed for central lead-lead collisions with $q_0=2{\text{GeV}}^2/\text{fm}$.

Figure 7

The same as in Fig. 6, but for production of a $\psi \left(2S\right)$ radial excitation.

Figure 8

Ratio of production rates of $\psi \left(2S\right)$ to $J/\psi$ calculated for central lead-lead collisions with $q_0=2{\text{GeV}}^2/\text{fm}$.

Figure 9

Azimuthal asymmetry parameter $v_2$ for $J/\psi$ production in lead-lead collisions calculated with $q_0=2{\text{GeV}}^2/\text{fm}$. The curves represent different centralities, from bottom to top $10\%,30\%$, and $60\%$.