Logarithmic corrections to O($a$) and O($a^2$) effects in lattice QCD with Wilson or Ginsparg-Wilson quarks

TL;DR

This paper derives the asymptotic behavior of lattice spacing effects in spectral quantities of lattice QCD with Wilson and Ginsparg-Wilson quarks, highlighting the role of logarithmic corrections and their impact on lattice artifacts.

Contribution

It provides a detailed derivation of the asymptotic lattice spacing dependence including logarithmic corrections for various quark discretizations in lattice QCD.

Findings

Leading order lattice artifacts are not severely logarithmically enhanced for Nf ≤ 4.

A dense spectrum of leading powers may cause pile-ups and cancellations.

The computational strategy for 1-loop anomalous dimensions is detailed.

Abstract

We derive the asymptotic lattice spacing dependence $a^n[2b_0\bar{g}^2(1/a)]^{\hat{\Gamma}_i}$ relevant for spectral quantities of lattice QCD, when using Wilson, O$(a)$ improved Wilson or Ginsparg-Wilson quarks. We give some examples for the spectra encountered for $\hat{\Gamma}_i$ including the partially quenched case, mixed actions and using two different discretisations for dynamical quarks. This also includes maximally twisted mass QCD relying on automatic O$(a)$ improvement. At O$(a^2)$, all cases considered have $\min_i\hat{\Gamma}_i\gtrsim -0.3$ if $N_\mathrm{f}\leq 4$, which ensures that the leading order lattice artifacts are not severely logarithmically enhanced in contrast to the O$(3)$ non-linear sigma model [1,2]. However, we find a very dense spectrum of these leading powers, which may result in major pile-ups and cancellations. We present in detail the computational strategy employed to obtain the 1-loop anomalous dimensions already used in [3].