Heavy quark transport in heavy ion collisions at energies available at the BNL Relativistic Heavy Ion Collider and at the CERN Large Hadron Collider within the UrQMD hybrid model

We implement a Langevin approach for the transport of heavy quarks in the ultrarelativistic quantum molecular dynamics (UrQMD) hybrid model, which uses the transport model UrQMD to determine realistic initial conditions for the hydrodynamical evolution of quark gluon plasma and heavy charm and bottom quarks. It provides a realistic description of the background medium for the evolution of relativistic heavy ion collisions. The diffusion of heavy quarks is simulated with a relativistic Langevin approach, using two sets of drag and diffusion coefficients, one based on a $T$-matrix approach and one based on a resonance model for elastic scattering of heavy quarks within the medium. In the case of the resonance model we investigate the effects of different decoupling temperatures of heavy quarks from the medium, ranging between 130 and $180\mathrm{MeV}$. We present calculations of the nuclear modification factor $R_{AA}$, as well as of the elliptic flow $v_2$ in Au + Au collisions at $\sqrt{s_{NN}}=200\text{GeV}$ and Pb + Pb collisions at $\sqrt{s_{NN}}=2.76\mathrm{TeV}$. To make our results comparable to experimental data at the Relativistic Heavy Ion Collider (RHIC) and Large Hadron Collider (LHC), we implement a Peterson fragmentation and a quark coalescence approach followed by semileptonic decay of the D and B mesons to electrons. We find that our results strongly depend on the decoupling temperature and the hadronization mechanism. At a decoupling temperature of $130\mathrm{MeV}$ we reach a good agreement with the measurements at both the RHIC and the LHC energies simultaneously for the elliptic flow $v_2$ and the nuclear modification factor $R_{AA}$.

Figure 1

Drag (left) and diffusion (right) coefficients in the resonance model and the T-matrix approach for charm and bottom quarks. The plot shows the dependence of the coefficients on the three-momentum $|\vec{p}|$ at a fixed temperature $T=180\text{MeV}$.

Figure 2

Drag (left) and diffusion (right) coefficients in the resonance model and the T-matrix approach for charm and bottom quarks. The plot shows the dependence of the coefficients on the temperature at a fixed three-momentum $|\vec{p}|=0.8\text{GeV}$. The T-matrix coefficients are calculated between 180 and $360\text{MeV}$ only.

Figure 3

Fits of D- and ${\mathrm{D}}^{*}$-meson $p_T$ spectra in $200\text{A}\text{GeV}$ d-Au collisions at the RHIC with a modified PYTHIA simulation (left) and the corresponding nonphotonic single-electron $p_T$ spectra in pp and d-Au collisions (taken from [40]) (right). The missing yield of high-$p_T$ electrons is fitted with the analogous B-meson decay spectra, thus fixing the bottom-to-charm ratio at ${\sigma }_{b\overline{b}}/{\sigma }_{c\overline{c}}\simeq 4.9\times {10}^{-3}$.

Figure 4

Left: Elliptic flow, $v_2$, of heavy quarks in Au + Au collisions at $\sqrt{s_{NN}}=200\mathrm{GeV}$. We use a rapidity cutoff of $\left|y\right|<0.35$. Thick lines depict charm quarks, while thin lines depict bottom quarks. Right: Elliptic flow, $v_2$, of electrons from heavy meson decays using Peterson fragmentation to D/B mesons and subsequent decay into electrons in Au + Au collisions at $\sqrt{s_{NN}}=200\mathrm{GeV}$. We use a rapidity cutoff of $\left|y\right|<0.35$. Data are from [48].

Figure 5

Left: $R_{AA}$ of heavy quarks in Au + Au collisions at $\sqrt{s_{NN}}=200\mathrm{GeV}$. We use a rapidity cutoff of $\left|y\right|<0.35$. Thick lines depict charm quarks, while thin lines depict bottom quarks. Right: $R_{AA}$ of electrons from heavy quark decays in Au + Au collisions at $\sqrt{s_{NN}}=200\mathrm{GeV}$ compared to RHIC data [48]. We use a rapidity cutoff of $\left|y\right|<0.35$. The high-$p_T$ suppression turns out to be too strong compared with the data.

Figure 6

Elliptic flow $v_2$ (left) and $R_{AA}$ (right) of D mesons using different ${\epsilon }_Q$ values in the Peterson fragmentation function.

Figure 7

Left: Elliptic flow, $v_2$, of heavy quarks in Au + Au collisions at $\sqrt{s_{NN}}=200\mathrm{GeV}$ employing a $k$ factor of 3. We use a rapidity cutoff of $\left|y\right|<0.35$. Thick lines depict charm quarks, while thin lines depict bottom quarks. Right: Elliptic flow, $v_2$, of electrons from heavy quark decays in Au + Au collisions at $\sqrt{s_{NN}}=200\mathrm{GeV}$ employing a $k$ factor of 3. We use a rapidity cutoff of $\left|y\right|<0.35$. The flow in our calculation using a $k$ factor is comparable to the data [48].

Figure 8

Left: $R_{AA}$ of electrons from heavy flavor decays in Au + Au collisions at $\sqrt{s_{NN}}=200\mathrm{GeV}$ employing a $k$ factor of 3. We use a rapidity cutoff of $\left|y\right|<0.35$. Thick lines show the results for charm quarks, and thin lines for bottom quarks. Right: $v_2$ of electrons from heavy flavor decays in Au + Au collisions at $\sqrt{s_{NN}}=200\mathrm{GeV}$ employing a $k$ factor of 3. We use a rapidity cutoff of $\left|y\right|<0.35$. As expected the medium modification is stronger than without a $k$ factor. Data are taken from [48].

Figure 9

Elliptic flow $v_2$ (left) and $R_{AA}$ (right) of D mesons (thick lines) and B mesons (thin lines) in Au + Au collisions at $\sqrt{s_{NN}}=200\mathrm{GeV}$. We use a rapidity cutoff of $\left|y\right|<0.35$. A comparison of Peterson fragmentation and coalescence with light quarks is shown. For the drag and diffusion coefficients we use the resonance model with a decoupling temperature of 150 MeV.

Figure 10

Elliptic flow $v_2$ (left) and nuclear modification factor $R_{AA}$ (right) of electrons from heavy quark decays in Au + Au collisions at $\sqrt{s_{NN}}=200\mathrm{GeV}$ using a coalescence mechanism. We use a rapidity cutoff of $\left|y\right|<0.35$. For a decoupling temperature of $130\mathrm{MeV}$ we find a reasonable agreement with the data [48].

Figure 11

Elliptic flow $v_2$ (left) and nuclear modification factor $R_{AA}$ (right) of heavy quarks in Au + Au collisions at $\sqrt{s_{NN}}=200\mathrm{GeV}$. We use a rapidity cutoff of $\left|y\right|<0.35$. Different equations of state are compared.

Figure 12

Comparison between calculations with averaged initial conditions and calculations with fluctuating event-by-event initial conditions for the hydrodynamic stage. Left: Elliptic flow $v_2$ of heavy quarks in Au + Au collisions at $\sqrt{s_{NN}}=200\mathrm{GeV}$. Right: Nuclear modification factor $R_{AA}$ of heavy quarks in Au + Au collisions at $\sqrt{s_{NN}}=200\mathrm{GeV}$. Parameters are $k=1$ and $T_{\text{freeze-out}}=150$ MeV.

Figure 13

Left: Flow $v_2$ of D mesons in Pb + Pb collisions at $\sqrt{s_{NN}}=2.76\mathrm{TeV}$ compared to data from the ALICE experiment [57]. A rapidity cutoff of $\left|y\right|<0.35$ is employed. Right: $R_{AA}$ of D mesons in Pb-Pb collisions at $\sqrt{s_{NN}}=2.76\mathrm{TeV}$ compared to experimental data from ALICE [58]. A rapidity cutoff of $\left|y\right|<0.35$ is employed.

Figure 14

Left: Comparison of the drag coefficients for charm quarks between the Nantes approach (“HTL”) and our approach (”$T$-Matrix” and “Resonance”). Right: Comparison of the diffusion coefficients for charm quarks between the Nantes approach and our approach.

Figure 15

Left: Comparison of the elliptic flows of charm quarks for different drag and diffusion coefficients. Right: Comparison of the nuclear modification factors of charm quarks for different drag and diffusion coefficients. As in all previous numerical simulations, even in this case the diffusion coefficients $B_1$ and $B_0$ are computed from the drag coefficient $A$ using (21).

Figure 16

Left: Comparison of the elliptic flows of charm quarks for different drag and diffusion coefficients. Right: Comparison of the nuclear modification factors of charm quarks for different drag and diffusion coefficients. In the numerical simulations performed to produce these plots, only the $B_1$ coefficients are computed from the $A$ coefficients using (21), while the $B_0$ coefficients are taken from the underlying models for the HQ scattering cross sections.

Figure 17

Elliptic flow $v_2$ (left) and nuclear modification factor $R_{AA}$ (right) of D and B mesons using Peterson fragmentation in Au + Au collisions at $\sqrt{s_{NN}}=200\mathrm{GeV}$. We use a rapidity cutoff of $\left|y\right|<0.35$.

Figure 18

Elliptic flow $v_2$ (left) and nuclear modification factor $R_{AA}$ (right) of D and B mesons using Peterson fragmentation and a $k$ factor of 3 in Au + Au collisions at $\sqrt{s_{NN}}=200\mathrm{GeV}$. We use a rapidity cutoff of $\left|y\right|<0.35$.

Figure 19

Elliptic flow $v_2$ (left) and nuclear modification factor $R_{AA}$ (right) of D and B mesons using coalescence in Au + Au collisions at $\sqrt{s_{NN}}=200\mathrm{GeV}$. We use a rapidity cutoff of $\left|y\right|<0.35$.