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Charmonia with different transverse momentum $p_T$ usually comes fromdifferent mechanisms in the relativistic heavy ion collisions. This work triesto review the theoretical studies on quarkonium evolutions in the deconfinedmedium produced in p-Pb and Pb-Pb collisions. The charmonia with high $p_T$ aremainly from the initial hadronic collisions, and therefore sensitive to theinitial 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 aremainly produced by the recombination of charm and anti-charm quarks in themedium. In the extremely low $p_T\sim 1/R_A$ ($R_A$ is the nuclear radius),additional contribution from the coherent interactions between electromagneticfields generated by one nucleus and the target nucleus plays a non-negligiblerole in the $J/\psi$ production even in semi-central Pb-Pb collisions.

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