Non-equilibrium Dynamical Attractors and Thermalisation of Charm Quarks in Nuclear Collisions at the LHC Energy

Abstract

We study the non-equilibrium dynamics, thermalisation and attractor behaviour of charm quarks in a longitudinally expanding Quark-Gluon Plasma within the Relativistic Boltzmann Transport approach in 1+1D Bjorken expansion. Considering both a strong AdS/CFT coupling scenario with constant $2\pi T{D}_s=1$ and a temperature-dependent diffusion coefficient $D_s^{\text{lQCD}}(T)$ from the recent unquenched lattice QCD data, we analyse the evolution of effective temperature, momentum moments and distribution functions for different initial conditions, including FONLL and EPOS4HQ spectra. We find that charm quarks exhibit dynamical attractors; however, the temperature dependence of $D_s^{\text{lQCD}}(T)$ leads to significantly longer relaxation times compared to the strong coupling limit. While dynamical attractors occur within $\sim 1-1.5\mathrm{fm}$ for $2\pi T{D}_s=1$, they are delayed to $\sim 5\mathrm{fm}$ for $D_s^{\text{lQCD}}(T)$, becoming comparable to the lifetime of the Quark-Gluon Plasma phase in ultra-relativistic collisions. This indicates that charm quarks may not fully thermalise, especially in small systems such as peripheral or light-ion collisions. We further show that, for $D_s^{\text{lQCD}}(T)$, the deviation from equilibrium becomes as large as $\delta f_{HQ}/f_{eq}\sim p_T^{\beta }\sim \mathcal{O}(1)$ already at $p_T\simeq 3\mathrm{GeV}$, rising with $\beta \sim 4.5$, thus questioning the applicability of viscous hydrodynamics to charm dynamics.