Coupled charm and charmonium transport in a strongly coupled quark-gluon plasma

The quark-gluon plasma (QGP) is a strongly coupled medium in which both open and hidden charm particles experience substantial nonperturbative interactions. This poses a major challenge for a quantitative description of charmonium transport in ultra-relativistic heavy-ion collisions, as it requires a mutually consistent treatment of pertinent transport coefficients. In this work, we present a coupled charm-charmonium transport framework for a strongly coupled QGP based on thermodynamic $T$-matrix interactions with recent constraints from Wilson-line correlators (WLCs) computed in lattice QCD. For the first time, the same underlying heavy-light interactions and in-medium spectral functions are used to self-consistently evaluate charm-quark diffusion and charmonium kinetics. In particular, the charmonium equilibrium limit, a critical transport parameter for regeneration, is evaluated in the presence of broad spectral functions. Charm-quark diffusion is simulated via Langevin dynamics and coupled to a Boltzmann equation for charmonium dissociation and regeneration. The equilibrium limit of the statistical model is recovered once charm quarks thermalize, and its extension to describe off-equilibrium is constructed. Preliminary applications to charmonium observables in Pb-Pb collisions at the LHC capture the measured centrality and momentum dependence fairly well.

💡 Research Summary

The paper presents a unified transport framework for open‑charm (c‑quarks) and hidden‑charm (charmonium) states in a strongly coupled quark‑gluon plasma (sQGP). The authors build on a thermodynamic T‑matrix approach whose underlying heavy‑light interaction potentials are constrained by Wilson‑line correlators (WLCs) calculated in lattice QCD. By employing the same T‑matrix for both charm‑quark scattering and charmonium binding, the model ensures a self‑consistent description of diffusion coefficients, spectral functions, and reaction rates.

Charm‑quark dynamics are simulated with a relativistic Langevin equation. The drag coefficient Γ(p) and momentum‑diffusion coefficient D(p) are linked through the Einstein relation, and both are derived from the heavy‑light T‑matrix. The resulting relaxation rate A(p) exhibits a strong temperature and momentum dependence, especially an enhancement at low momentum that reproduces the large non‑perturbative interaction strength inferred from lattice QCD without the need for ad‑hoc K‑factors.

Charmonium evolution is treated with a Boltzmann transport equation that contains a dissociation term α and a regeneration term β. Both rates are obtained from the same half‑off‑shell T‑matrix using a quasifree approximation: the 2→3 dissociation process is reduced to an effective 2→2 scattering of a thermal parton off one of the heavy quarks, while the other heavy quark acts as a spectator. The binding energy of the charmonium state is incorporated via an effective charm‑quark mass ˜m_c = m_c – E_B^Ψ, which is itself extracted from the T‑matrix. Momentum sharing between the charm and anticharm quarks is proportional to their effective masses, guaranteeing equal velocities and exact energy‑momentum conservation.

A central achievement of the work is the formulation of the equilibrium limit in the presence of broad in‑medium spectral functions. By enforcing detailed balance, the ratio β/α reproduces the statistical‑model equilibrium abundance when charm quarks have thermalized, while still allowing a controlled off‑equilibrium description when they have not. The broad spectral widths, rather than destroying bound states, actually extend the temperature range over which resonant correlations survive, thereby widening the regeneration window.

The coupled framework is applied to Pb–Pb collisions at LHC energies (√s_NN = 5.02 TeV) using a schematic fireball evolution that incorporates a lattice‑QCD‑compatible equation of state. Initial charm‑quark spectra, cold‑nuclear‑matter effects, and the time‑dependent temperature profile are fed into the Langevin and Boltzmann equations. The resulting nuclear modification factors R_AA for J/ψ and ψ(2S) reproduce the measured centrality dependence and the characteristic rise of R_AA at low transverse momentum, reflecting regeneration, while the suppression at high p_T is dominated by primordial production and dissociation. The model also captures the stronger suppression of excited states, a consequence of their larger in‑medium widths.

In summary, the authors deliver the first transport model that simultaneously treats charm‑quark diffusion and charmonium kinetics with a common, lattice‑constrained non‑perturbative interaction. The approach bridges the gap between microscopic heavy‑light dynamics and macroscopic observables, offering a robust tool for probing the strongly coupled nature of the QGP. Future extensions to full 3‑D hydrodynamic backgrounds and to bottomonium will further test the universality of the method.