The asymptotic approach to the continuum of lattice QCD spectral observables

TL;DR

This paper analyzes the asymptotic behavior of discretization errors in spectral quantities of lattice QCD using various fermion formulations, proposing tree-level O(a^2) improvement to enhance accuracy.

Contribution

It provides a detailed asymptotic analysis of cutoff effects across multiple lattice QCD fermion actions and advocates for tree-level O(a^2) improvement for better continuum extrapolation.

Findings

Wilson fermions and DWF have similar asymptotic cutoff effects.

Large mass-dependent effects occur with certain domain wall heights.

Tree-level O(a^2) improvement enhances asymptotic behavior.

Abstract

We consider spectral quantities in lattice QCD and determine the asymptotic behavior of their discretization errors. Wilson fermion with O$(a)$-improvement, (M\"obius) Domain wall fermion (DWF), and overlap Dirac operators are considered in combination with the commonly used gauge actions. Wilson fermions and DWF with domain wall height $M_5=1+{\rm O}(g_0^2)$ have the same, approximate, form of the asymptotic cutoff effects: $ K\,a^2\left[\bar g^2(a^{-1})\right]^{0.760}$. A domain wall height $M_5=1.8$, as often used, introduces large mass-dependent $K'(m)\,a^2\left[\bar g^2(a^{-1})\right]^{0.518}$ effects. Massless twisted mass fermions have the same form as Wilson fermions when the Sheikholeslami-Wohlert term [1] is included. For their mass-dependent cutoff effects we have information on the exponents $\hat\Gamma_i$ of $\bar g^2(a^{-1})$ but not for the pre-factors. For staggered fermions there is only partial information on the exponents. We propose that tree-level ${\rm O}(a^2)$ improvement, which is easy to do [2], should be used in the future -- both for the fermion and the gauge action. It improves the asymptotic behavior in all cases.