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We systematically investigate the collisional energy loss ($-dE/dz$) and momentum diffusion coefficients ($\kappa_{T/L}$) of heavy quarks traversing the quark-gluon plasma (QGP) across diverse temperature scales. By employing the soft-hard factorization model, we first compute the transport properties at leading order in the QCD coupling, demonstrating that the full results eliminate the dependence on the arbitrary intermediate separation scale $t^*$. This framework is systematically extended to finite quark chemical potential ($\mu \neq 0$), revealing a pronounced enhancement of transport coefficients in baryon-rich environments. To bridge the gap between the high-temperature perturbative domain and the strongly coupled crossover region ($T \rightarrow T_c$), we incorporate non-perturbative dynamics via two complementary approaches. The introduction of a temperature-dependent Polyakov loop background in a semi-QGP effective theory yields a distinct suppression of the energy loss due to reduced color density. Furthermore, by synthesizing short-range Yukawa screening with a long-range confining string tension into a unified, lattice-constrained interaction kernel, we completely circumvent the traditional reliance on soft-hard momentum cutoffs. This unified non-perturbative model successfully captures the extreme medium opacity near $T_c$, predicting a spatial diffusion coefficient $2\pi T D_{s} \approx 0.5 \sim 1.7$ that exhibits striking quantitative agreement with recent lattice QCD extractions. Ultimately, our results provide a robust and comprehensive dynamical interpretation of heavy-flavor transport spanning both perturbative and non-perturbative regimes.
[1] Jiale Lou, Wu Wang, Jiazhen Peng, Fei Sun, Kejun Wu, Wei Xie, Zuman Zhang, Shuang Li, and Sa Wang, Soft-Hard Factorization of Heavy-Quark Transport in QCD Matter at Finite Chemical Potential, Phys. Rev. D 112, 116001 (2025)
[2] Jiazhen Peng, Kewei Yu, Shuang Li, Wei Xiong, Fei Sun, Wei Xie, Unraveling the collisional energy loss of a heavy quark in a quark-gluon plasma, Phys. Rev. D 109, 096028 (2024)
[3] Wu Wang, Yuqi Luo, Fei Sun, Sa Wang, Jungang Deng, Wei Xie, Shuang Li, and Kejun Wu, Heavy-quark transport across the QCD crossover driven by a lattice-constrained in-medium potential, arXiv: 2604.10889
[4] Jiazhen Peng, Jiale Lou, Fei Sun, Kejun Wu, Wei Xie, Zuman Zhang, Shuang Li, and Sa Wang, Perturbative and non-perturbative properties of heavy quark transport in a thermal QCD medium, arXiv:2510.10294
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