Toward the determination of heavy-quark transport coefficients in quark-gluon plasma

Several transport models have been employed in recent years to analyze heavy-flavor meson spectra in high-energy heavy-ion collisions. Heavy-quark transport coefficients extracted from these models with their default parameters vary, however, by up to a factor of 5 at high momenta. To investigate the origin of this large theoretical uncertainty, a systematic comparison of heavy-quark transport coefficients is carried out between various transport models. Within a common scheme devised for the nuclear modification factor of charm quarks in a brick medium of a quark-gluon plasma, the systematic uncertainty of the extracted drag coefficient among these models is shown to be reduced to a factor of 2, which can be viewed as the smallest intrinsic systematical error band achievable at present time. This indicates the importance of a realistic hydrodynamic evolution constrained by bulk hadron spectra and of heavy-quark hadronization for understanding the final heavy-flavor hadron spectra and extracting heavy-quark drag coefficient. The transverse transport coefficient is less constrained due to the influence of the underlying mechanism for heavy-quark medium interaction. Additional constraints on transport models such as energy loss fluctuation and transverse-momentum broadening can further reduce theoretical uncertainties in the extracted transport coefficients.

Figure 1

Calculations of (a) $A$ and (b) $\widehat{q}/T^3$, compared between different groups with a common setup in the left columns, and different setups (within the CCNU-LBNL model) in the right columns (setup 1, $t-{\mu }_{\mathrm{D}}^2$ regulator with quantum statistics; setup 2, $t<-{\mu }_{\mathrm{D}}^2$ cutoff with quantum statistics; setup 3, $t-{\mu }_{\mathrm{D}}^2$ regulator with classical statistics).

Figure 2

Model calculations of the $D$ meson $R_{\mathrm{AA}}$ (a) with “tune 1” parameters (see Table 4) in central Pb-Pb collisions at 2.76 ATeV and (b) Au-Au collisions at 200 AGeV as compared to experimental data [129, 130, 131].

Figure 3

The momentum dependence of (a) $A$ and (b) $\widehat{q}/T^3$. Left columns (“basic”) are direct calculations from different models; and right (“tune 1”) are extracted from comparing to data with different models.

Figure 4

The temperature dependence of (a) $A$ and (b) $\widehat{q}/T^3$. Left columns (“basic”) are direct calculations from different models and right (“tune 1”) are extracted from comparing to data with different models.

Figure 5

The nuclear modification factor of charm quark in a static medium at $t=2$ and 4 fm, using the tune 1 setup in each model that provides the best description of experimental data.

Figure 6

Correlation between the heavy quark $R_{\mathrm{AA}}$ and the “anisotropy” extracted from the $R_{\mathrm{AA}}$ at 2 and 4 fm in a static medium.

Figure 7

Common baseline of charm quark $R_{\mathrm{AA}}$ in a brick with model parameters denoted as “tune 2” in this work.

Figure 8

Time evolution of charm quark $R_{\mathrm{AA}}$ within the common brick.

Figure 9

Transport coefficients extracted from the common baseline of $R_{\mathrm{AA}}$ in a brick: (a) $A$, (b) elastic contribution to $A$, and (c) $\widehat{q}/T^3$.

Figure 10

Time evolution of (a) average energy, (b) average transverse momentum broadening, and (c) longitudinal momentum fluctuation of heavy quarks inside a common static medium.

Figure 11

Calculations of (a) $A$, (b) elastic contribution to $A$, and (c) $\widehat{q}/T^3$, at $T=200$ MeV and 300 MeV with tune 2.