Regularizing QCD with staggered fermions and the fourth root trick

TL;DR

This paper examines the non-locality of staggered-fermion lattice QCD with the fourth root trick at finite lattice spacing, showing it becomes local and consistent with continuum QCD in the limit as the lattice spacing approaches zero.

Contribution

It provides a renormalization-group argument demonstrating the restoration of taste symmetry and locality in the continuum limit for this lattice QCD formulation.

Findings

Non-locality at finite lattice spacing due to taste symmetry breaking

Restoration of taste symmetry in the continuum limit

Validity of staggered chiral perturbation theory with the replica trick for effective descriptions

Abstract

We investigate the properties of staggered-fermion lattice QCD in which the fourth root of the fermion determinant is taken. We show that this theory is non-local at non-zero lattice spacing $a$, and that the non-locality is caused by the breaking of taste symmetry at $a\ne 0$. We then present a renormalization-group based argument that the theory restores taste symmetry in the continuum limit. As a consequence the theory is local in that limit, and falls into the correct universality class. Finally, we argue that the correct effective theory for the physics of Goldstone bosons at $a\ne 0$ is given by staggered chiral perturbation theory with the replica trick.