# Charmonium production in a thermalizing heat bath

## TL;DR

This paper extends the Remler formalism to study charmonium production in thermalizing environments, incorporating temperature-dependent effects and quark-antiquark separation dynamics to align with statistical model predictions.

## Contribution

It introduces two additional rates to the Remler formalism, accounting for temperature effects and quark-antiquark separation, improving its applicability to heavy-ion collision scenarios.

## Key findings

- The modified rates align the formalism with statistical model results.
- Temperature dependence of Wigner density affects charmonium formation.
- Quark-antiquark separation dynamics are crucial for accurate modeling.

## Abstract

Using the Remler formalism for the creation of composed particles, we study charmonium production both in thermalized and thermalizing boxes, which contain charm and anticharm quarks. The thermalizing box studies include the lowering of the box temperature, the spatial diffusion of charm and anticharm quarks, which are initially confined in the central region, as well as the combination of both, what imitates heavy-ion collisions. Comparing numerical and analytical results we demonstrate that the rate of the original Remler formalism has to be supplemented by two rates to obtain, for $t\to \infty$, results, which are consistent with the statistical model predictions: i) a rate, which takes into account the temperature dependence of the Wigner density of the quarkonium during the expansion and, in the case that a heavy quark potential is not implemented in the Monte Carlo approach, ii) a rate which comes from the change of the relative distance between the heavy quark and antiquark. These results provide the basis for future applications of the Remler formalism to heavy-ion collisions.