  We present results for matching factors for staggered four-fermion operators
constructed using HYP-smeared fat links both in the action and the operators.
  We use perturbation theory to calculate the matching factors and work to
one-loop order. The new feaure of this work is the use of the Symanzik-improved
gauge action, as opposed to the Wilson gauge action. Our results are needed for
our ongoing calculation of weak matrix elements using HYP-smeared staggered
valence quarks and operators on MILC lattices. We give explicit results for
matching factors of the operator needed to calculate $B_K$. We compare the
impact of the improvement of the gauge action on one-loop coefficients with
that of mean-field improvement of the operators.
