# Theoretical Review of Charmonium Production with Different $p_T$ in the Hot Medium

## TL;DR

This paper reviews theoretical models of charmonium production at various transverse momenta in hot deconfined media created in heavy ion collisions, highlighting different mechanisms and sensitivities to initial conditions.

## Contribution

It provides a comprehensive review of the mechanisms of charmonium production across different $p_T$ ranges in relativistic heavy ion collisions.

## Key findings

- High $p_T$ charmonia originate mainly from initial collisions.
- Charmonia with $0.1<p_T<5$ GeV/c are mainly produced by recombination.
- Coherent electromagnetic interactions significantly affect low $p_T$ $J/eta$ production.

## Abstract

Charmonia with different transverse momentum $p_T$ usually comes from different mechanisms in the relativistic heavy ion collisions. This work tries to review the theoretical studies on quarkonium evolutions in the deconfined medium produced in p-Pb and Pb-Pb collisions. The charmonia with high $p_T$ are mainly from the initial hadronic collisions, and therefore sensitive to the initial energy density of the bulk medium. For those charmonia within $0.1<p_T<5$ GeV/c at the energies of Large Hadron Collisions (LHC), They are mainly produced by the recombination of charm and anti-charm quarks in the medium. In the extremely low $p_T\sim 1/R_A$ ($R_A$ is the nuclear radius), additional contribution from the coherent interactions between electromagnetic fields generated by one nucleus and the target nucleus plays a non-negligible role in the $J/\psi$ production even in semi-central Pb-Pb collisions.