On the fourth root prescription for dynamical staggered fermions

TL;DR

This paper investigates the theoretical foundations of using the fourth root of the staggered fermion determinant in Lattice QCD, proposing a candidate Dirac operator with acceptable locality in the free field case.

Contribution

It introduces a simple candidate Dirac operator that satisfies the fourth root relation in free fields and analyzes its locality properties, addressing a key theoretical issue.

Findings

Candidate Dirac operator satisfies the fourth root relation in free fields

Operator exhibits acceptable exponential locality as lattice spacing approaches zero

Discussion on extending the approach to interacting fields

Abstract

With the aim of resolving theoretical issues associated with the fourth root prescription for dynamical staggered fermions in Lattice QCD simulations, we consider the problem of finding a viable lattice Dirac operator D such that (det D_{staggered})^{1/4} = det D. Working in the flavour field representation we show that in the free field case there is a simple and natural candidate D satisfying this relation, and we show that it has acceptable locality behavior: exponentially local with localisation range vanishing ~ (a/m)^{1/2} for lattice spacing a -> 0. Prospects for the interacting case are also discussed, although we do not solve this case here.