Impact of off-shell dynamics on the transport properties and the dynamical evolution of charm quarks at RHIC and LHC temperatures

We evaluate drag and diffusion transport coefficients comparing a quasi-particle approximation with on-shell constituents of the QGP medium and a dynamical quasi-particles model with off-shell bulk medium at finite temperature T. We study the effects of the width $$\gamma $$ γ of the particles of the bulk medium on the charm quark transport properties exploring the range where $$\gamma < M_{q,g}$$ γ < M q , g . We find that off-shell effects are in general quite moderate and can induce a reduction of the drag coefficient at low momenta that disappear already at moderate momenta, $$p \gtrsim $$ p ≳ 2–3 GeV. We also observe a moderate reduction of the breaking of the fluctuation–dissipation theorem (FDT) at finite momenta. Moreover, we have performed a first study of the dynamical evolution of HQ elastic energy loss in a bulk medium at fixed temperature extending the Boltzmann (BM) collision integral to include off-shell dynamics. A comparison among the Langevin dynamics, the BM collisional integral with on-shell and the BM extension to off-shell dynamics shows that the evolution of charm energy when off-shell effects are included remain quite similar to the case of the on-shell BM collision integral.