  We use Soft Collinear Effective Theory (SCET) to analyze the transverse
momentum broadening, or diffusion in transverse momentum space, of an energetic
parton propagating through quark-gluon plasma. Since we neglect the radiation
of gluons from the energetic parton, we can only discuss momentum broadening,
not parton energy loss. The interaction responsible for momentum broadening in
the absence of radiation is that between the energetic (collinear) parton and
the Glauber modes of the gluon fields in the medium. We derive the effective
Lagrangian for this interaction, and we show that the probability for picking
up transverse momentum k_\perp is given by the Fourier transform of the
expectation value of two transversely separated light-like path-ordered Wilson
lines. This yields a field theoretical definition of the jet quenching
parameter \hat q, and shows that this can be interpreted as a diffusion
constant. We close by revisiting the calculation of \hat q for the strongly
coupled plasma of N=4 SYM theory, showing that previous calculations need some
modifications that make them more straightforward and do not change the result.
