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

One loop matching factors for improved staggered four-fermion operators with improved glue