# Improvement of the Staggered Fermion Operators

## TL;DR

This paper derives finite lattice spacing corrections for staggered fermion operators, demonstrating the absence of order a terms in the improved action and proposing a general method to remove O(a) corrections from matrix elements.

## Contribution

It provides a detailed derivation of lattice corrections and introduces a general program to improve fermion operators, removing O(a) errors from their matrix elements.

## Key findings

- No O(a) corrections in Symanzik improved action
- Fermion bilinear matrix elements have O(a) corrections
- B_K matrix element does not have O(a) corrections

## Abstract

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.