# Probing the transport properties of Quark-Gluon Plasma via heavy-flavor Boltzmann and Langevin dynamics

## TL;DR

This study compares Boltzmann and Langevin dynamics in modeling heavy quark transport in quark-gluon plasma, revealing differences in transport coefficients and their impact on observables like energy loss, R_AA, and v_2, with implications for experimental data interpretation.

## Contribution

It provides a systematic comparison of Boltzmann and Langevin approaches for heavy quark transport, highlighting their differences and compatibility with experimental data.

## Key findings

- Boltzmann coefficients are larger at high T and energy.
- Langevin dynamics predict greater energy loss and smaller R_AA.
- Boltzmann approach yields larger v_2 and azimuthal broadening.

## Abstract

The heavy quark propagation behavior inside the quark-gluon plasma (QGP), is usually described in terms of the Boltzmann dynamics, which can be reduced to the Langevin approach by assuming a small momentum transfer for the scattering processes between heavy quarks and the QGP constituents. In this work, the temperature and energy dependence of the transport coefficients are calculated in the framework of both Boltzmann and Langevin dynamics. The derived transport coefficients are found to be systematically larger in the Boltzmann approach as compared with the Langevin, in particular in the high temperature and high energy region. Within each of the two theoretical frameworks, we simulate the charm quark production and the subsequent evolution processes in relativistic heavy-ion collisions. We find that the total in-medium energy loss is larger from the Langevin dynamics, resulting in a smaller (larger) $R_{\rm AA}$ at high (low) $p_{\rm T}$, for both the charm quark and heavy-flavor mesons. Meanwhile, the Boltzmann model is found to induce larger $v_{\rm 2}$, in particular at moderate $p_{\rm T}$, as well as stronger broadening behavior for the azimuthal distributions. By comparing the model calculations with available experimental measurements for D-mesons, we find that the Langevin approach is more favored by the $R_{\rm AA}$ data while the Boltzmann approach is more favored favor by the $v_{\rm 2}$ data. A simultaneous description of both observables appear challenging for both models.