Perturbative improvement of staggered fermions using fat links

TL;DR

This paper investigates how fat links can be used to improve staggered fermions by reducing perturbative corrections, establishing theoretical equivalences, and proposing new construction methods for better lattice QCD simulations.

Contribution

It proves key theorems on SU(3) projection and shows the equivalence of renormalization between different fat link constructions at one loop level.

Findings

Renormalization is identical for SU(3) projected Fat7 and hypercubic links.

SU(3) projection can be viewed as tadpole improvement.

Alternative fat link constructions are proposed for further research.

Abstract

We study possibility of improving staggered fermions using various fat links in order to reduce perturbative corrections to the gauge-invariant staggered fermion operators. We prove five theorems on SU(3) projection, triviality in renormalization, multiple SU(3) projections, uniqueness and equivalence. As a result of these theorems, we show that, at one loop level, the renormalization of staggered fermion operators is identical between SU(3) projected Fat7 links and hypercubic links, as long as the action and operators are constructed by imposing the same perturbative improvement condition. In addition, we propose a new view of SU(3) projection as a tool of tadpole improvement for the staggered fermion doublers. As a conclusion, we present alternative choices of constructing fat links to improve the staggered fermion action and operators, which deserve further investigation.