Logarithmic corrections to O($a^2$) effects in lattice QCD with unrooted Staggered quarks

TL;DR

This paper derives the asymptotic lattice-spacing dependence for spectral quantities in lattice QCD with unrooted Staggered quarks, clarifying the effects of logarithmic corrections and operator contributions.

Contribution

It provides a detailed derivation of the $a^2$ dependence with logarithmic corrections for spectral quantities in lattice QCD using unrooted Staggered quarks, including clarifications on operator effects.

Findings

Derived asymptotic $a^2$ dependence with logarithmic corrections.

Quantified the dependence for different numbers of flavors ($N_f=0,4,8,12$).

Clarified the role of mass-dimension 5 operators and $ ext{O}(a)$ effects.

Abstract

We derive the asymptotic lattice-spacing dependence $a^2[2b_0\bar{g}^2(1/a)]^{\hat{\gamma}_i}$ relevant for spectral quantities of lattice QCD, when using unrooted Staggered quarks. Without taking any effects from matching into account we find $\min_i\hat{\gamma}_i\approx -0.273, -0.301, -0.913, -2.614$ for $N_\mathrm{f}=0,4,8,12$ respectively. Common statements in the literature on the absence of mass-dimension~5 operators from the on-shell basis of the Symanzik Effective Field Theory action are being clarified for a description using strictly local tastes, here playing the role of continuum quark flavours. Potential impact of $\mathrm{O}(a)$ EOM-vanishing terms beyond spectral quantities is being discussed.