Universality and Quark Masses of the Staggered Fermion Action

TL;DR

This paper examines the properties of staggered fermions in lattice QCD, highlighting that taste breaking causes an additive mass shift, preventing simulations from reaching the chiral limit at finite lattice spacing.

Contribution

It demonstrates that the quark mass in the flavor symmetric theory differs from the staggered mass due to taste breaking, affecting the interpretation of lattice results.

Findings

Additive mass shift due to taste breaking.

Staggered fermions cannot reach the chiral limit at finite lattice spacing.

Finite lattice spacing simulations correspond to heavier quark masses.

Abstract

Staggered fermions with 4 tastes are expected to describe 4-flavor QCD in the continuum limit, therefore at finite lattice spacing the staggered determinant should be equivalent to an SU(4) flavor-symmetric system up to lattice artifacts. This equivalence is the starting point of the 4th root trick used to reduce the number of fermion flavors and provides the only consistent description of 2 or 1 flavor systems. In this paper we argue that the quark mass of the underlying flavor symmetric theory differs from the staggered mass by an additive term due to the taste breaking of the staggered action. The relation is the same for 2 and 1 flavor fermions. This additive mass shift implies that at finite lattice spacing staggered simulations correspond to heavier quark masses than indicated by the staggered Goldstone pion and that staggered fermions cannot reach the chiral limit at finite lattice spacing.