In this work, we report on our computation results for the best value of the shear viscosity to entropy ratio of quark–gluon plasma produced in the relativistic Au–Au collisions at 200 GeV. Time evolution of heavy quarks distribution functions is calculated by solving the Fokker–Planck evolution equation using the new technique: Iterative Laplace transform method. We compute the drag and diffusion coefficients by considering the hard thermal loop corrections and also temperature dependence running strong coupling, up to complete interactions of leading order.

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