Renormalization of the Lattice HQET Isgur-Wise Function

We compute the perturbative renormalization factors required to match to the continuum Isgur-Wise function, calculated using lattice Heavy Quark Effective Theory. The velocity, mass, wavefunction and current renormalizations are calculated for both the forward difference and backward difference actions for a variety of velocities. Subtleties are clarified regarding tadpole improvement, regulating divergences, and variations of techniques used in these renormalizations.