{Quasi particle model vs lattice QCD thermodynamics: extension to $N_f=2+1+1$ flavors and momentum dependent quark masses}

In the last decade a Quasi-Particle Model (QPM) has supplied the basis for the study of HQ production in ultra-relativistic AA collisions, allowing for a phenomenological estimate of the HQ diffusion coefficient D-s(T). Taking advantage of the new lattice QCD results for the Equation of State (EoS) with 2+1+1 dynamical flavors, we extend our QPM approach from N-f=2+1 to N-f=2+1+1, in which the charm quark is included. Given an effective coupling g(T) fixed by a fit to the lQCD energy density & varepsilon;(T), we evaluate the impact of different temperature parametrizations of charm quark mass on EoS and susceptibilities chi(q)(T) of light, chi(s)(T) of strange and chi(c)(T) of charm quarks, the last favouring a charm quark mass increasing toward T-c. We also explore the extension of the QPM approach to a more realistic approach, that we label QPM(p), in which quark and gluon masses explicitly depend on their momentum converging to the current quark mass at high momenta, as expected from asymptotic free dynamics. The QPM(p) is seen to allow for a simultaneous quantitative description not only of the EoS but also of the quark susceptibilities (chi(q)(T), chi(s)(T)), which instead are underestimated in the simple QPM model. Furthermore, evaluating the spatial diffusion coefficient 2 pi TDs(T) in the QPM(p), we find it is also significantly closer than QPM to the recent lQCD data performed including dynamical fermions. Finally, in a 1+1D expanding system, we evaluate the R-AA(pT) in the QPM and QPM(p), finding a significant reduction at low momenta for QPM(p) which could lead in a realistic scenario to a better agreement to experimental data.