  We compute the correction to the energy loss of a hard parton due to short
separation distances between the creation of the particle and the in-medium
scattering center that stimulates bremsstrahlung radiation, to first order in
opacity. In deriving the result we make full use of the large formation time
assumption, which results in a significant reduction of the number of diagrams
contributing to the small separation distance correction. An asymptotic
analysis of our small separation distance correction term finds that the
correction dominates at large $\sim 100$ GeV parent parton energies; scales
like $L$ with the size of the system for small $L$, but like $L^0$ at larger
$L$; and breaks color triviality. An extensive numerical investigation of the
correction term confirms the aforementioned analytic findings, reveals that the
correction term does not go to zero for large $L$, finds that the correction is
sensitive to the mass of the parent parton, and shows a crucial dependence of
the energy loss on a proper treatment of the physics of separation distances on
the order of the Debye screening length. However, an examination of the large
formation time approximation shows that it is violated for much of the phase
space of the emitted radiation, implying a need to investigate the sensitivity
of jet quenching results from relaxing this approximation. Our result
constitutes an important step toward understanding partonic energy loss in
small colliding systems.
