Boltzmann dynamics and temperature dependence of energy loss: Towards an understanding of the RAA and v2 puzzle for D-Mesons

The two key observables related to heavy quarks that have been measured in experiments are the nuclear suppression factor RAA and the elliptic flow v2. Reproducing these two observables simultaneously is a puzzle which have challenged all the existing models. We have studied two ingredients responsible to address a large part of such a puzzle: the temperature dependence of the energy loss and the full solution of the Boltzmann collision integral for the scattering between the heavy quarks and the particle of the bulk. We have considered four different models to evaluate the temperature dependence of drag and diffusion coefficients of the heavy quark. All these four different models are set to reproduce the same RAA(pT) measured in experiments at RHIC and LHC energy. We have found that for the same RAA(pT) one can generate 2-3 times more v2 depending on the temperature dependence of the heavy quarks drag coefficient. Moreover comparing the Fokker-Planck and the Boltzmann approach we have found that the latter seems more efficient into reproducing the elliptic flow for the same RAA. Even a larger difference between the two approaches emerges from the comparison of a more differential observable, the angular correlation.