  I look at propagation of jets that act as a probe of the medium in the
phenomenologically relevant case of a short lived dilute Quark Gluon
Plasma(QGP) created during heavy ion collisions. Working in the regime where
the lifetime of the medium is of the order or smaller than the formation time
of the energetic jet, I derive a factorization formula with a manifest
separation of scales for an illustrative jet substructure observable using the
Open Quantum system Effective Field Theory(EFT) approach developed in
\cite{Vaidya:2020lih}, in terms of a medium structure function and a medium
induced jet function . The medium structure function or the "PDF of the medium"
that describes the observable independent physics of the QGP remains identical
to that in a dilute long lived medium considered in \cite{Vaidya:2021vxu},
while the medium induced jet function is modified and incorporates quantum
interference between the hard interaction that creates the jet and subsequent
medium interactions. The medium jet function continues to enjoy a BFKL rapidity
evolution just as for a long lived medium, albeit with a modified
renormalization scale that now depends on the medium lifetime.
