Charm quark evolution in the early stages of heavy-ion collisions

Heavy quarks are predominantly generated at the initial stage of relativistic heavy-ion collisions such that heavy flavor observables have the potential to provide information on the pre-equilibrium medium dynamics. In this study, we investigate the sensitivity of D-meson $R_{AA}$ and $v_2$ to early-time charm quark dynamics in Pb+Pb collisions at $\sqrt{s_{NN}}=5.02$ TeV. We employ the IP-Glasma+MUSIC+UrQMD framework to model the evolution of the bulk medium. Charm quarks are generated using PYTHIA with nuclear parton distribution functions and evolved using Langevin dynamics within MARTINI. We observe that even though there is significant momentum broadening in the earliest stage, D-meson $R_{AA}$ and $v_2$ are only weakly sensitive to pre-equilibrium interactions.

💡 Research Summary

In this work the authors investigate how the very early, pre‑equilibrium stage of relativistic heavy‑ion collisions influences the final‑state observables of charm quarks, specifically the nuclear modification factor (R_AA) and elliptic flow (v₂) of D‑mesons in Pb+Pb collisions at √sₙₙ = 5.02 TeV. The study employs a state‑of‑the‑art multi‑stage simulation framework: IP‑Glasma generates the fluctuating color‑glass‑condensate (CGC) initial conditions and evolves the Glasma fields via classical Yang‑Mills equations; at τ = 0.4 fm/c the system is handed over to the viscous hydrodynamic code MUSIC, which solves the DNMR second‑order equations with temperature‑dependent shear (η/s) and bulk (ζ/s) viscosities tuned to soft‑hadron data. The hydrodynamic freeze‑out surface is sampled with the iSS Cooper‑Frye sampler, and the subsequent hadronic cascade is modeled with UrQMD.

Charm quarks are produced in the initial hard scatterings using PYTHIA, with nuclear parton distribution functions (EPS09) and isospin effects incorporated. For each IP‑Glasma event, tens of thousands of c c̄ pairs are sampled at the binary‑collision positions. A formation time τ_F = 1/m_c is imposed; before this time the pair is bound by a Cornell potential, after which the quarks are allowed to interact with the medium.

The transport of charm quarks through both the Glasma and the QGP phases is described by Langevin dynamics as implemented in MARTINI. Local energy density from IP‑Glasma (or MUSIC) is converted to an effective temperature (ideal‑gas gluon EOS for Glasma, lattice‑QCD EOS for QGP). Drag η(p) and momentum‑diffusion coefficients κ_T, κ_L are obtained from the spatial diffusion coefficient D_s(T) computed in recent 2 + 1‑flavor lattice QCD studies. Using the Einstein relations κ = 2T²/D_s and η = T/(m_c D_s), the authors parametrize the momentum dependence of η and κ, reproducing the perturbative QCD trend: drag decreases with increasing momentum while diffusion rises and saturates at high p.

Hadronization occurs at T_h = 165 MeV. The authors first apply a modified color‑evaporation model to form charmonium states, then treat the remaining charm quarks with a hybrid fragmentation‑coalescence scheme. Coalescence probabilities are calculated using Gaussian Wigner functions with a width parameter σ derived from a harmonic‑oscillator picture; the overall coalescence strength N_coal is fixed to 0.2 to match experimental D‑meson spectra.

The key result is that, despite sizable momentum broadening of charm quarks during the first ≲0.2 fm/c of Glasma evolution, the impact on final‑state D‑meson R_AA and v₂ is modest. Varying the formation time or the strength of the early‑stage interaction changes R_AA by less than 5 % and v₂ by less than 0.01, both well within current experimental uncertainties. The authors conclude that the short lifetime of the pre‑equilibrium phase, combined with the dominant diffusion and energy loss occurring later in the QGP, renders D‑meson observables largely insensitive to the details of the earliest stage. This finding justifies the common practice of neglecting explicit pre‑equilibrium heavy‑quark transport in phenomenological model‑to‑data comparisons, while also providing a quantitative baseline for future Bayesian analyses that may wish to incorporate early‑time dynamics. The paper highlights the importance of a consistent multi‑stage treatment and suggests that more precise low‑p_T measurements or refined Glasma modeling would be required to uncover any subtle pre‑equilibrium signatures in heavy‑flavor observables.