Multiple scattering of heavy-quarks in dense matter and the parametric prominence of drag

Abstract: The case of heavy quark propagation in dense extended matter is studied in the multiple scattering formalism of the higher twist energy loss scheme. We consider the case of deep inelastic scattering off a large nucleus. The hard lepton scatters off a heavy quark fluctuation within one of the nucleons. This heavy quark then propagates through the dense medium, multiply scattering off the gluon field of the remaining nucleons in its path. We consider the fictitious process where a heavy quark propagates through the nucleus without radiation. Invoking Soft-Collinear Effective Theory power counting arguments, we consider the case of a "semi-hard" heavy-quark where the mass is of the order of the out-going momentum and larger than the transverse momentum imparted per unit length due to scattering. In this limit, it is found that longitudinal momentum exchanges (quantified by the transport coefficient $\hat{e}$) have a comparable effect on the off-shellness of the propagating quark, as the transverse momentum exchanges (quantified by $\hat{q}$) which constitute the leading cause of off-shellness for propagating light quarks or gluons. Consequences of this new hierarchy for the propagation of the heavy quark in dense matter are discussed.