Calculating the Jet Transport Coefficient $\widehat{q}$ in Lattice Gauge Theory

The formalism of jet modification in the higher twist approach is modified to describe a hard parton propagating through a hot thermalized medium. The leading order contribution to the transverse momentum broadening of a high energy (near on-shell) quark in a thermal medium is calculated. This involves a factorization of the perturbative process of scattering of the quark from the non-perturbative transport coefficient. An operator product expansion of the non-perturbative operator product which represents $\widehat{q}$ is carried out and related via dispersion relations to the expectation of local operators. These local operators are then evaluated in quenched SU(2) lattice gauge theory.