Estimating the charm quark diffusion coefficient and thermalization time from $D$ meson spectra at energies available at the BNL Relativistic Heavy Ion Collider and the CERN Large Hadron Collider

We describe the propagation of charm quarks in the quark-gluon plasma (QGP) by means of a Boltzmann transport approach. Nonperturbative interaction between heavy quarks and light quarks have been taken into account through a quasiparticle approach in which light partons are dressed with thermal masses tuned to lattice quantum chromodynamics (lQCD) thermodynamics. Such a model is able to describe the main feature of the nonperturbative dynamics: the enhancement of the interaction strength near $T_c$. We show that the resulting charm in-medium evolution is able to correctly predict simultaneously the nuclear suppression factor, $R_{\text{AA}}$, and the elliptic flow, $v_2$, at both Relativistic Heavy Ion Collider and Large Hadron Collider (LHC) energies and at different centralities. The hadronization of charm quarks is described by mean of an hybrid model of fragmentation plus coalescence and plays a key role toward the agreement with experimental data. We also performed calculations within the Langevin approach, which can lead to very similar $R_{\text{AA}}\left(p_T\right)$ as Boltzmann, but the charm drag coefficient as to be reduced by about a $30\%$ and also generates an elliptic flow $v_2\left(p_T\right)$ is about a $15\%$ smaller. We finally compare the space diffusion coefficient $2\pi T{D}_s$ extracted by our phenomenological approach to lattice QCD results, finding a satisfying agreement within the present systematic uncertainties. Our analysis implies a charm thermalization time, in the $p\to 0$ limit, of about $4–6\text{fm}/\text{c}$, which is smaller than the QGP lifetime at LHC energy.

Figure 1

Drag coefficients as a function of temperature obtained within the Boltzmann transport approach and Langevin dynamics to describe the same experimental data (shown in Fig. 4).

Figure 2

The $p_T$ distribution of $D$ mesons, obtained from the fragmentation of charm quarks in $p+p$ collisions, are compared with the experimental data from the STAR Collaboration, taken from Ref. [54].

Figure 3

The $p_T$ distribution of $D^0$ and $D^{+}$ mesons, obtained from the fragmentation of charm quarks in $p+p$ collisions, are compared with the experimental data from the ALICE Collaboration,taken from Ref. [53]. The experimental points are an extrapolation from 7 to 2.76 TeV.

Figure 4

$D$ meson $R_{\text{AA}}$ in $Au+Au$ collisions at $\sqrt{s}=200\mathrm{AGeV}$ and centrality $0–10\%$ compared to STAR data. Experimental data has been taken from Ref. [58].

Figure 5

$D$ meson $R_{\text{AA}}$ in $Au+Au$ collisions at $\sqrt{s}=200\mathrm{AGeV}$ and centrality $10–40\%$ compared to STAR data. Experimental data has been taken from Ref. [58].

Figure 6

Coalescence probability for a charm going to one of the mesons $\left(D^{+},D^0,D^{*0},D^{+*}\right)$ as a function of transverse momentum at RHIC and LHC.

Figure 7

$D$ meson elliptic flow in $Au+Au$ collisions at $\sqrt{s}=200\mathrm{AGeV}$ and centrality $0–80\%$ compared to STAR data. Experimental data has been taken from Ref. [61].

Figure 8

Single electron elliptic flow in $Au+Au$ collisions at $\sqrt{s}=200\mathrm{AGeV}$ in minimum bias compared to PHENIX data. Experimental data has been taken from Ref. [8].

Figure 9

$D$ meson $R_{\text{AA}}$ in $Pb+Pb$ collisions at $\sqrt{s}=2.76\mathrm{ATev}$ and centrality $0–20\%$ compared to ALICE data. Experimental data has been taken from Ref. [62].

Figure 10

$D$ meson $R_{\text{AA}}$ in $Pb+Pb$ collisions at $\sqrt{s}=2.76\mathrm{ATev}$ and centrality $30–50\%$ compared to ALICE data. Experimental data has been taken from Ref. [62].

Figure 11

$D$ meson elliptic flow in $Pb+Pb$ collisions at $\sqrt{s}=2.76\mathrm{ATeV}$ and centrality $30–50\%$ compared to ALICE data. Experimental data has been taken from Ref. [63].

Figure 12

Spatial diffusion coefficient as a function of temperature obtained within the Boltzmann transport approach and Langevin dynamics to describe experimental data, along with the results from lattice QCD. We have also shown the results obtained within other models. Spatial diffusion coefficient for the QPM model employed to prediction for $R_{\text{AA}}$ and $v_2$ within a Boltzmann (BM) dynamics (green solid line) and with a Langevin (LV) one (orange dashed line) [30]; by symbols quenched lQCD [73] (circles) [74] (square); model calculations based on LO pQCD [11, 12] (solid and dashed brown lines) and AdS/CFT rescaled to match the energy density of QCD plasma [71]; in dotted line is shown the $D_s$ coefficient for $D$ meson in hadronic matter [67].