This paper offers a new, self-consistent way to describe how heavy quarks (charm and bottom) move through the quark–gluon plasma as the system passes the QCD crossover temperature. The authors build a single interaction rule that mixes ordinary (perturbative) short-range forces with strong, non-perturbative long-range forces. They tune that interaction to lattice QCD results so it does not rely on an arbitrary separation between “soft” and “hard” collisions.

Concretely, the interaction is derived from an in-medium heavy-quark potential that includes a short-range screened Coulomb piece (a Yukawa form, meaning it falls off quickly with distance) and a long-range confining “string” piece (which models the force that tries to keep quarks together). The vacuum parameters are fixed by averaging across lattice ensembles, giving a short-distance coupling of about 0.406, a string scale with sqrt(σ)=0.495 GeV, and a constant shift V0≈2.356 GeV. The authors fit a temperature-dependent screening mass MD(T) to lattice data using a Hard Thermal Loop inspired formula with two fitted coefficients (κ1≈0.686, κ2≈−0.317) and provide upper and lower parameter sets to quantify uncertainty.

They transform the coordinate-space potential into momentum space and use that as an effective mediator of scattering between a heavy quark and light thermal partons (quarks and gluons). This gives a single momentum-space kernel that smoothly covers both small and large momentum transfers. The construction is implemented at Born level (first-order scattering) and uses an instantaneous approximation. Those approximations are justified for heavy quarks because their mass is much larger than the medium temperature, so they move slowly and exchanges are dominated by spatial momentum.

Why this matters: near the crossover temperature Tc (chosen consistently with the lattice work as Tc=172.5 MeV) the medium shows strong non-perturbative effects that earlier weak-coupling calculations missed. Including the string contribution constrained by lattice data makes the medium far more opaque to heavy quarks. The model predicts a spatial diffusion coefficient 2πT Ds in the range about 0.5 to 1.7, in good quantitative agreement with recent lattice QCD extractions. A smaller diffusion coefficient means heavier drag, so the result gives a dynamical explanation for the strong coupling of heavy quarks near Tc.