  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.
