Quasi particle model vs lattice QCD thermodynamics: extension to \(N_f=2+1+1\) flavors and momentum dependent quark masses

Abstract

In the last decade a quasi-particle model (QPM) has supplied the basis for the study of heavy quark (HQ) production in ultra-relativistic collisions, allowing for a phenomenological estimate of the HQ diffusion coefficient \[D_s(T)\] . Using the new lattice QCD results for the equation of state (EoS) with 2+1+1 dynamical flavors, we extend the QPM from \[N_f=2+1\] to \[N_f=2+1+1\] , where the charm quark is included. Fixing the coupling g( T) by a fit to the lQCD energy density \[\epsilon (T)\] , 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 to a more realistic approach called QPM \[_p\] , where 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 \[_p\] allows 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. Furthermore, evaluating the spatial diffusion coefficient \[2\pi T D_s(T)\] in the QPM \[_p\] , we find it is also closer than QPM to the recent lQCD data performed including dynamical fermions. Finally, in a 1+1D expanding system, we evaluate the \[R_{AA}(p_T)\] 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.