Observable Dependence of Viscous Corrections in QGP: Heavy Quarks and Dileptons in Chapman--Enskog Theory

Abstract: We calculate, for the first time, heavy quark transport and thermal dilepton production from QGP using viscous correction up to second order in gradients. We use the form of viscous correction obtained from Chapman-Enskog like expansion of the Boltzmann transport equation in relaxation time approximation, and compare our results with that of Grad's 14-moment approximation. By employing the temperature and shear stress evolution profiles of QGP obtained from second-order causal relativistic viscous hydrodynamics, we study the heavy quark transport coefficients and thermal dilepton production from an evolving QGP. In the case of HQ transport, the CE corrections suppress the drag force substantially, induce a non-trivial momentum dependence in transverse momentum diffusion, and result in a comparatively less modification in longitudinal momentum diffusion. Whereas, for thermal dileptons, the CE corrections result in an enhanced early-time contribution which decreases and become converging to the first-order CE correction with the evolution of QGP, and remain well behaved compared to that of Grad's correction. Our results indicate that the modification of the observable due to viscous corrections is governed by the magnitude of the corrections as well as the interplay between their momentum dependence and momentum weighting of the transport and emission kernels. We demonstrate that the momentum structure of the various viscous corrections at the level of distribution function is not directly translated to the observables since the different observables are sensitive to distinct regions of momentum space.