Abstract
The relativistic diffusion process of heavy quarks is formulated on the basis of the relativistic Langevin equation in It\^o discretization scheme. The drag force inside the quark-gluon plasma (QGP) is parametrized according to the formula for the strongly coupled plasma obtained by the anti-de-Sitter space/conformal field theory (AdS/CFT) correspondence. The diffusion dynamics of charm and bottom quarks in QGP is described by combining the Langevin simulation under the background matter described by the relativistic hydrodynamics. Theoretical calculations of the nuclear modification factor ${R}_{\mathrm{AA}}$ and the elliptic flow ${v}_{2}$ for the single electrons from the charm and bottom decays are compared with the experimental data from the relativistic heavy-ion collisions. The ${R}_{\mathrm{AA}}$ for electrons with large transverse momentum (${p}_{T}>3$ GeV) indicates that the drag force from the QGP is as strong as the AdS/CFT prediction.
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