Improvement of the Staggered Fermion Operators

We present a complete and detailed derivation of the finite lattice spacing corrections to staggered fermion matrix elements. Expanding upon arguments of Sharpe, we explicitly implement the Symanzik improvement program demonstrating the absence of order $a$ terms in the Symanzik improved action. We propose a general program to improve fermion operators to remove $O(a)$ corrections from their matrix elements, and demonstrate this program for the examples of matrix elements of fermion bilinears and $B_K$. We find the former does have $O(a)$ corrections while the latter does not.