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

Abstract

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.

Figures (15)

• Figure 1: The charm-quark relaxation rate, $A(p)$, as a function of momentum at different temperatures from $T$-matrices constrained by WLCs from lattice QCD Tang:2023tkm.
• Figure 2: Schematic $T$-matrix diagrams illustrating the dissociation and regeneration of charmonium in the QGP. Upper panel: dissociation process $i\,\Psi \to i\,c\bar{c}$, in which a thermal parton $i$ scatters off a bound charmonium state $\Psi$, leading to its breakup into an unbound charm--anticharm pair. Lower panel: inverse process of regeneration $i\,c\bar{c} \to i\,\Psi$, where an uncorrelated $c\bar{c}$ pair recombines into charmonium through an interaction with a thermal parton. In both cases, the interaction is described by the half-off-shell $T$-matrix amplitude $T_{ci}$. The 3-momenta of the thermal partons and heavy quarks are indicated explicitly.
• Figure 3: Dissociation rates of three charmonium states calculated within the nonperturbative $T$-matrix formalism in the WLC scenarios, shown as functions of their momenta at different temperatures (different colors). From left to right, the panels correspond to $J/\psi$, $\chi_c$, and $\psi(2S)$.
• Figure 4: Charmonium dissociation rates at vanishing three-momentum as a function of temperature.
• Figure 5: Binding energies of $J/\psi$, $\chi_c$ and $\psi(2S)$ as a function of temperature, extracted from the in-medium $T$-matrix approach in the WLC scenario.