Heavy-quark transport across the QCD crossover driven by a lattice-constrained in-medium potential

We present a self-consistent framework for heavy-quark transport in the quark-gluon plasma across the QCD crossover region. By synthesizing perturbative and non-perturbative interactions into a unified interaction kernel, we circumvent the traditional reliance on arbitrary soft-hard momentum separation scales. The interaction is governed by an in-medium effective potential, incorporating short-range Yukawa screening and long-range confining string contributions, both rigorously constrained by the latest lattice QCD data. Our results reveal that the non-perturbative string tension is indispensable for capturing the extreme opacity of the medium near the critical temperature $T_c$. Specifically, our model predicts a spatial diffusion coefficient of $2\pi T{D}_s\approx 0.5\sim 1.7$, demonstrating a striking quantitative agreement with the recent lattice QCD extractions. Ultimately, our results provide a robust dynamical interpretation of the strong heavy-quark coupling near the QCD crossover and offer a unified framework for describing heavy-flavor transport in hot and dense QCD matter.