Renormalization-group analysis of the validity of staggered-fermion QCD with the fourth-root recipe

TL;DR

This paper develops a renormalization-group framework to analyze the validity of the fourth-root recipe in staggered-fermion lattice QCD, arguing it becomes valid in the continuum limit as taste-symmetry violations vanish.

Contribution

It introduces a renormalization-group blocking approach to justify the fourth-root recipe's validity in the continuum limit of lattice QCD with staggered fermions.

Findings

The fourth-root recipe is valid in the continuum limit.

Taste-symmetry violations vanish as lattice spacing approaches zero.

Reweighted theories approximate the fourth-root theory better near the continuum.

Abstract

I develop a renormalization-group blocking framework for lattice QCD with staggered fermions. Under plausible, and testable, assumptions, I then argue that the fourth-root recipe used in numerical simulations is valid in the continuum limit. The taste-symmetry violating terms, which give rise to non-local effects in the fourth-root theory when the lattice spacing is non-zero, vanish in the continuum limit. A key role is played by reweighted theories that are local and renormalizable on the one hand, and that approximate the fourth-root theory better and better as the continuum limit is approached on the other hand.