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We apply the Low's theorem to soft gluon emission from heavy quark scattering in the nonperturbative strongly interacting quark-gluon plasma (sQGP). The sQGP is described in terms of the dynamical quasi-particles and adjusted to reproduce the EoS from lQCD at finite temperature and chemical potential. Since the emitted gluon is soft and of long wavelength, it does not provide information on the detailed structure of the scattering, and only the emission from incoming and outgoing partons is enough. It simplifies the calculations making the scattering amplitude factorizable into the elastic scattering and the emission of soft gluon. Imposing a proper upper limit on the emitted gluon energy, we obtain the guage-invariant scattering cross sections of heavy quarks with the massive partons of the medium as well as their transport coefficients (momentum drag and diffusion) in the QGP and compare with those from the elastic scattering without gluon emission., 14 pages, 10 figures

We study the interaction of leading jet partons in a strongly interacting quark-gluon plasma (sQGP) medium based on the effective dynamical quasi-particle model (DQPM). The DQPM describes the non-perturbative nature of the sQGP at finite temperature $T$ and baryon chemical potential $\mu_B$ based on a propagator representation of massive off-shell partons (quarks and gluons) whose properties (characterized by spectral functions with $T,\mu_B$ dependent masses and widths) are adjusted to reproduce the lQCD EoS for the QGP in thermodynamic equilibrium. We present the results for the jet transport coefficients, i.e. the transverse momentum transfer squared per unit length $\hat{q}$ as well as the energy loss per unit length $\Delta E =dE/dx$, in the QGP and investigate their dependence on the temperature $T$ and baryon chemical potential $\mu_B$ as well as on jet properties such as the leading jet parton momentum, mass, flavor, and the choice of the strong coupling constant. In this first study only elastic scattering processes of a leading jet parton with the sQGP partons are explored discarding presently the radiative processes (such as gluon Bremsstrahlung). We present a comparison of our results for the elastic energy loss in the sQGP medium with the pQCD results obtained by the BAMPS and LBT models as well as with other theoretical approaches such as lattice QCD and the LO-HTL and also with estimates of $\hat{q}/T^3$ by the color string percolation model (CSPM) and the JET and JETSCAPE Collaborations based on a comparison of hydrodynamical calculations with experimental heavy-ion data., Comment: 15 pages, 9 figures