  I examine the regime of forward scattering of an energetic particle in a
Plasma medium in thermal equilibrium. Treating the particle as an open quantum
system interacting with a bath, I look at the time evolution of the reduced
density matrix of the system. The kinematic and dynamical time scales that
emerge can exist in several possible hierarchies which can lead to different
EFT formulations. I show that in certain hierarchies, it becomes necessary to
account for arbitrary number of coherent exchanges between the system and the
bath going beyond the independent scattering paradigm. Analytic results are
obtained in certain limits and the formalism is applied for the measurement of
transverse momentum broadening of a quark in a Quark Gluon Plasma medium.
