Transport coefficients of heavy quarks around $T_c$ at finite quark chemical potential

The interactions of heavy quarks with the partonic environment at finite temperature $T$ and finite quark chemical potential ${\mu }_q$ are investigated in terms of transport coefficients within the dynamical quasiparticle model (DQPM) designed to reproduce the lattice-QCD (lQCD) results (including the partonic equation of state) in thermodynamic equilibrium. These results are confronted with those of nuclear many-body calculations close to the critical temperature $T_c$. The hadronic and partonic spatial diffusion coefficients join smoothly and show a pronounced minimum around $T_c$ at ${\mu }_q=0$ as well as at finite ${\mu }_q$. Close to and above $T_c$ its absolute value matches the lQCD calculations for ${\mu }_q=0$. The smooth transition of the heavy-quark transport coefficients from the hadronic to the partonic medium corresponds to a crossover in line with lattice calculations, and differs substantially from perturbative-QCD calculations which show a large discontinuity at $T_c$. This indicates that in the vicinity of $T_c$ dynamically dressed massive partons should be the effective degrees of freedom in the quark-gluon plasma.

Figure 1

Spatial diffusion coefficient for heavy quarks, $D_s$, as a function of $T$ for ${\mu }_q=0$. Below $T=180$ MeV we display the hadronic diffusion coefficient from [14]; above $T=180$ MeV, that for a partonic environment. The solid orange line is the result of [6] while the red thick solid line shows the DpQCD prediction. The lattice calculations are from Ref. [15].

Figure 2

Adiabatic trajectories in the plasma and hadron phases as functions of $T$ and ${\mu }_B=3{\mu }_q$. For the plasma phase we present calculations in the DpQCD model as well as for massless partons. The trajectories in the hadron phase are taken from [14]. We display as well the transition temperature $T_c\left({\mu }_B\right)$ between the hadronic and plasma phases as given in the DQPM model.

Figure 3

Spatial diffusion constant $D_s$ as a function of $T$ for ${\mu }_q\ne 0$. $D_s$ is displayed for different values of $s/n_B$ for a hadronic environment [14] as well as for a partonic environment. For the latter, pQCD calculations [6] are compared with DpQCD calculations.

Figure 4

Energy loss per unit length, $dE/dx$, of a c-quark with incoming momentum of 10 GeV in the plasma rest frame as a function of the temperature and quark chemical potential.