  The jet transport coefficient $\hat{q}$ is the leading transport coefficient
that controls the modification of hard jets produced in heavy-ion collisions.
This coefficient is inherently non-perturbative, and hence, is challenging to
compute from first principles. In this report, we present a perturbative
quantum chromodynamics (pQCD) and lattice gauge theory based formulation to
study $\hat{q}$. We formulate $\hat{q}$ within a 4-dimensional (4D) quenched
SU(3) lattice. We consider a leading order diagram for a hard parton passing
through the quark-gluon plasma. The non-perturbative part is expressed in terms
of a non-local (two-point) Field-Strength-Field-Strength (FF) operator product
which can be Taylor expanded after analytic continuation to the Euclidean
region. Such an expansion allows us to write $\hat{q}$ in terms of the
expectation of local operators. Finally, we present our results for $\hat{q}$
in a pure gluon plasma.
