  A persistent and fascinating problem at the high energy colliders are jets.
Often trying to observe physics underlying the hard interactions at colliders
requires experimental cuts in phase space, defining several jet or beam
regions. QCD being a gauge theory that readily decays into infra-red modes,
correlations between jet regions is almost inevitable, spoiling the
predictivity of fixed order QCD calculations. One is faced with the task of
calculating the evolution of a reduced density matrix, where successively less
energetic (jet) regions are integrated out, to gain control of the calculation.
I relate the decay rates governing the flow into the IR to an effective field
theory expansion in soft jets, allowing a systematic and resummed calculation
of these rates, while further relating them to physically observable features
of the QCD cascade. To demonstrate the utility of the soft jet expansion, I
present a factorization theorem for a soft subjet collinearly splitting in and
out of a parent fat jet. Using the resummation properties of this factorization
theorem, I elucidate the structure of the subleading non-global logs (encoding
the jet correlations) in the hemisphere jet mass distribution, as well as give
a collinear improvement of the leading order resummation equation, the BMS
equation. I compare to other approaches to subleading resummation of NGLs, and
find the collinear improvement of the leading order equation removes the need
for kinematic-dependent corrections in the IR averaging procedure of the
reduced density matrix, so that no further large logs can be generated in the
IR. Finally I end with speculation about connections with collinear
improvements of the NLO B-JIMWLK hierarchy for small-$x$ resummation.
