Heavy Quark Energy Loss in the Hybrid Model

TL;DR

This work extends the Hybrid strong/weak coupling model to include heavy quarks, introducing a composite energy-loss description that smoothly bridges ultrarelativistic and non-relativistic regimes and a Local Color Neutralization mechanism for in-medium hadronization. By integrating perturbative production, holographic-inspired drag, Gaussian momentum diffusion, and in-medium recombination, the model delivers a coherent description of heavy-flavor observables across $R_{AA}$, $v_2$, and heavy baryon-to-meson ratios, matching data for charm and bottom hadrons and $b$-jets across centralities and $p_T$. The results indicate partial charm thermalization at low $p_T$ but non-negligible bottom non-thermalization, with the choice $\kappa_{HQ} \approx 4.4$ providing a reasonable balance between energy loss and flow, and emphasize the role of hadronization dynamics in shaping heavy-flavor observables. Overall, the paper establishes a unified framework to study heavy flavor and jet dynamics in QGP and points to future Bayesian analyses and improvements in diffusion modeling and hadronization treatment to further constrain transport properties of the QGP.

Abstract

Heavy quarks offer an invaluable hard probe of the droplets of quark gluon plasma (QGP) formed in heavy ion collisions at the LHC and RHIC. Given their large mass, they are predominantly produced in hard scattering processes at the earliest moment of a collision and given their rarity they almost never annihilate with a heavy antiquark subsequently. This means that they experience, and probe, the entire history of the expanding, cooling, droplet of QGP from hydrodynamization through hadronization. Quantitative measurements of heavy quark final state observables therefore give us access to information about the transport properties of QGP as well as about medium modifications of hadronization. To date, the Hybrid strong/weak coupling Model of jet quenching has not included any implementation of the heavy-quark sector, which has made it impossible to confront its predictions with measurements of heavy quark and jet observables together, in a unified fashion. Here, we extend the Hybrid Model to investigate heavy quark observables for the first time. We introduce a strongly-coupled calculation of heavy-quark energy loss with the correct behavior when the heavy quarks are either ultrarelativistic or non-relativistic, Gaussian momentum broadening, and recombination of heavy quarks with medium partons using a local color neutralization model of hadronization. We compare our results for the suppression $R_{\rm AA}$ and azimuthal anisotropies $v_2$ of B- and D-mesons and $Λ_c$ baryons, the $R_{\rm AA}$ of B-tagged jets, as well as baryon-to-meson ratios, with available experimental data from ALICE, ATLAS and CMS.

Figures (14)

• Figure 1: Comparison of how charm quarks (heavy quarks with $M=1.5$ GeV, left panels) and bottom quarks (heavy quarks with $M=4.75$ GeV, right panels) with initial energy 50 GeV (top panels) or 20 GeV (bottom panels) lose energy as a function of the distance $x$ that they have traveled through a "brick" of strongly coupled plasma with a constant temperature $T=200$ MeV. In all panels, the heavy quark initially loses energy as a light quark does. In all cases we have taken the parameter that controls the magnitude of light quark energy loss to be $\kappa_{\rm sc}=0.404$, as fit to data in Ref. Casalderrey-Solana:2018wrw. Curves with different colors correspond to different choices of $\kappa_{\rm HQ}$. The black curves show $dE/dx$ for a massless quark with initial energy $E_{\rm in}$, for reference. In all cases, the heavy quark comes to rest after traveling a finite distance, but in some cases this happens beyond the plot. The gray dotted line shows $E=M$, the energy of the heavy quark at rest.
• Figure 2: (Left) Charm quark spectrum from the FONLL calculation Cacciari:1998it compared to our reweighted PYTHIA8. The reweighting is such that the error bands approximate the error bars of the FONLL calculation. This plot confirms that our reweighting works as intended. (Right) Prompt $D^0$ spectrum in pp collisions obtained from PYTHIA8, after reweighting the charm quark spectrum to agree with the FONLL calculation as in the left panel, compared to ALICE measurements from Ref. ALICE:2021mgk. As in the left panel, the error band quantifies the FONLL uncertainty; additional statistical errors from our Monte Carlo simulation are smaller than the thickness of the dark red line.
• Figure 3: An illustration of the LCN hadronization model, applied in this paper to the production of charmed hadrons at freezeout. Each heavy quark recombines with the closest opposite color charge. The latter can be an antiquark, in which case recombination eventually yields a charmed meson, or it can be a diquark, in which case recombination yields a charmed baryon in the final state. In either case, as the heavy quark recombines with a light antiquark or diquark coming from the QGP the resulting color-singlet cluster picks up some momentum from the collective flow of the expanding droplet of QGP.
• Figure 4: Fraction of $D^0$ mesons with a given $p_T$ in the 0-5% centrality class that formed either via LCN recombination or via fragmentation as described by PYTHIA 8. Almost every $D^0$ meson with $p_T$ less than about twice its mass (which is to say most $D^0$ mesons) form via recombination. At these low values of $p_T$ (and also at intermediate $p_T$), the momentum that the charm quark picks up from the flowing droplet of QGP via recombination with a light antiquark contributes significantly to the momentum and, we shall see, to the $v_2$ of the $D^0$ mesons.
• Figure 5: Results from Hybrid Model calculations with $\kappa_{\rm HQ}=4.4$ of the suppression $R_{\rm AA}$ of $D^0$ mesons in PbPb collisions at $\sqrt{s_{\rm NN}}=5.02$ TeV compared to ALICE ALICE:2021rxaALICE:2021mgk and CMS CMS:2017qjw data. Hybrid Model calculations and ALICE data use a rapidity cut of $|y|<0.5$, while the CMS data is for $|y|<1$. The left (right) panels show the suppression of prompt (non-prompt) $D^0$ mesons, originating from $c$-quarks ($b$-quarks) propagating in the droplet of QGP. The upper (lower) panels are for 0-10% (30-50%) centrality collisions. For each experimental data point, we have added the statistical and systematic uncertainties in quadrature. For each Hybrid Model calculation, the darker (fainter) band shows the statistical uncertainties (uncertainties coming from FONLL reweighting of the $c$-quark production spectra).