# Probing the transport properties of quark-gluon plasma via heavy-flavor Boltzmann and Langevin dynamics

Li, Shuang (College of Science, China Three Gorges University, Yichang 443002, China) (Physics Department and Center for Exploration of Energy and Matter, Indiana University, 2401 N Milo B. Sampson Lane, Bloomington, Indiana 47408, USA) (Key Laboratory of Quark and Lepton Physics (MOE), Central China Normal University, Wuhan 430079, China) ; Wang, Chaowen (College of Science, China Three Gorges University, Yichang 443002, China) ; Wan, Renzhuo (Nano Optical Material and Storage Device Research Center, School of Electronic and Electrical Engineering, Wuhan Textile University, Wuhan 430200, China) ; Liao, Jinfeng (Physics Department and Center for Exploration of Energy and Matter, Indiana University, 2401 N Milo B. Sampson Lane, Bloomington, Indiana 47408, USA)

29 May 2019

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, by considering only the elastic scattering processes to have a better comparison and understanding of these two models. The extracted transport coefficients are found to be 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 energy loss due to elastic scattering is larger from the Boltzmann dynamics, resulting in a smaller ${R}_{\mathrm{AA}}$ at high ${p}_{T}$ (${p}_{T}\gtrsim 10\phantom{\rule{0.28em}{0ex}}\mathrm{GeV}$), for both the charm quark and heavy-flavor mesons. The Boltzmann model produces systematically larger ${v}_{2}$, in particular at moderate ${p}_{T}$, meanwhile, it shows a stronger broadening behavior for the relative azimuthal angle between initially back-to-back generated $c\overline{c}$ pairs in the similar region. They are mainly induced by the stronger interactions between heavy quarks and the QGP partons in Boltzmann, which are able to transfer more ${v}_{2}$ from the medium to the heavy quarks, as well as to pull more $c\overline{c}$ pairs from high momentum to low momentum. By comparing the model calculations with available experimental measurements for D mesons, a visible deviation can be observed for both the Boltzmann and Langevin approaches. The missing inelastic contributions allow reducing the discrepancy with data, and additionally, the relevant Langevin approach is more favored by the ${R}_{\mathrm{AA}}$ data while the Boltzmann approach is more favored favor by the ${v}_{2}$ data. A simultaneous description of both observables appears challenging for both models.

Published in: Physical Review C 99 (2019)