Observations on the Wilson fermions in the epsilon regime

TL;DR

This paper investigates the behavior of Wilson fermions in the low quark mass epsilon regime, analyzing cutoff effects, zero-mode interactions, and providing formulas to fit lattice data for better physical constant extraction.

Contribution

It introduces modified continuum epsilon regime formulas incorporating leading cutoff effects for Wilson fermions, aiding in systematic error estimation and removal.

Findings

Transition from small to large cutoff effects with decreasing quark mass.

Derived formulas for partition function and correlators including cutoff effects.

Guidelines for fitting lattice data to extract physical constants and reduce discretization errors.

Abstract

We make several observations concerning the low quark mass region with Wilson fermions and how this is connected with the epsilon regime in the continuum. A transition from tiny cutoff effects to rather large discretization errors would take place in general with Wilson fermions if we lower the quark mass at finite lattice spacing. We argue that these two regions exhibit rather different behaviours concerning the coupling between cutoff effects and zero-modes. We interpolate between these two regimes adding to the continuum epsilon regime formulae, in the spirit of the Symanzik expansion, the relevant operators parametrising the leading cutoff effects. We compute the partition function, the chiral condensate, scalar and pseudo-scalar correlation functions. The final formulae can be used to fit lattice data to extract physical low energy constants, and to estimate systematic uncertainties coming from discretization errors. Moreover they suggest ways on how to remove these cutoff effects, the core of which are captured by the continuum zero modes.