Power-counting theorem for staggered fermions

TL;DR

This paper extends lattice power-counting to QCD with staggered fermions, overcoming previous difficulties and generalizing the theorem to accommodate the unique challenges posed by staggered fermions.

Contribution

It generalizes Reisz's lattice power-counting theorem to include staggered fermions, addressing prior assumptions that failed for this fermion formulation.

Findings

Identifies limitations in Reisz's original proof for staggered fermions.

Develops a generalized power-counting theorem applicable to staggered fermions.

Provides a framework for analyzing lattice QCD with staggered fermions.

Abstract

Lattice power-counting is extended to QCD with staggered fermions. As preparation, the difficulties encountered by Reisz's original formulation of the lattice power-counting theorem are illustrated. One of the assumptions that is used in his proof does not hold for staggered fermions, as was pointed out long ago by Luscher. Finally, I generalize the power-counting theorem, and the methods of Reisz's proof, such that the difficulties posed by staggered fermions are overcome.