  The elastic energy loss encountered by jets produced in deep-inelastic
scattering (DIS) off a large nucleus is studied in the collinear limit. In
close analogy to the case of (non-radiative) transverse momentum broadening,
which is dependent on the medium transport coefficient $\hat{q}$, a class of
medium enhanced higher twist operators which contribute to the non-radiative
loss of the forward light-cone momentum of the jet ($q^-$) are identified and
the leading correction in the limit of asymptotically high $q^-$ is isolated.
Based on these operator products, a new transport coefficient $\hat{e}$ is
motivated which quantifies the energy loss per unit length encountered by the
hard jet. These operator products are then computed, explicitly, in the case of
a similar hard jet traversing a deconfined quark-gluon-plasma (QGP) in the
hard-thermal-loop (HTL) approximation. This is followed by an evaluation of
sub-leading contributions which are suppressed by the light-cone momentum
$q^-$, which yields the longitudinal "straggling" i.e., a slight change in
light cone momentum due to the Brownian propagation through a medium with a
fluctuating color field.
