# Staggered fermions and their $O(a)$ improvements

## TL;DR

This paper demonstrates the elimination of order $a$ errors in staggered fermion actions and operators through Symanzik improvement, enhancing the precision of lattice QCD calculations involving fermion bilinears and $B_K$.

## Contribution

It explicitly implements the Symanzik improvement for staggered fermions and proposes a general method to improve fermion operators, including currents.

## Key findings

- No order $a$ terms in the improved staggered fermion action.
- A systematic program to remove $O(a)$ corrections from fermion matrix elements.
- Identification of additional operators needed for current improvement.

## Abstract

Expanding upon the arguments of Sharpe, we explicitly implement the Symanzik improvement program demonstrating the absence of order $a$ terms in the staggered fermion 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 also determine the additional operators which must be added to improve the staggered fermion currents.