Logarithmic corrections to O(a) and O() effects in lattice QCD with Wilson or Ginsparg–Wilson quarks

Nikolai Husung

doi:10.1140/epjc/s10052-023-11258-8

2023 Impact factor 4.2

Particles and Fields

Open Access

This article has an erratum: [https://doi.org/10.1140/epjc/s10052-023-11392-3]

Eur. Phys. J. C (2023) 83: 142
https://doi.org/10.1140/epjc/s10052-023-11258-8

Regular Article - Theoretical Physics

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

Nikolai Husung¹^,2^a

¹ Physics and Astronomy, University of Southampton, University Road, SO17 1BJ, Southampton, UK
² Deutsches Elektronen-Synchrotron DESY, Platanenallee 6, 15738, Zeuthen, Germany

^a n.husung@soton.ac.uk

Received: 13 June 2022
Accepted: 23 January 2023
Published online: 14 February 2023

Abstract

We derive the asymptotic lattice spacing dependence $a^{n} {[2 b_{0} {\bar{g}}^{2} (1 / a)]}^{{\hat{Γ}}_{i}}$ $a^n[2b_0\bar{g}^2(1/a)]^{\hat{\Gamma }_i}$ relevant for spectral quantities of lattice QCD, when using Wilson, $O (a)$ $\textrm{O}(a)$ improved Wilson or Ginsparg–Wilson quarks. We give some examples for the spectra encountered for ${\hat{Γ}}_{i}$ $\hat{\Gamma }_i$ 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 $O (a)$ $\textrm{O}(a)$ improvement. At $O (a^{2})$ $\textrm{O}(a^2)$ , all cases considered have ${min}_{i} {\hat{Γ}}_{i} ≳ - 0.3$ $\min _i\hat{\Gamma }_i\gtrsim -0.3$ if $N_{f} \leq 4$ $N_{\textrm{f}}\le 4$ , which ensures that the leading order lattice artifacts are not severely logarithmically enhanced in contrast to the O(3) non-linear sigma model (Balog et al. in Nucl Phys B 824:563–615, 2010; Balog et al. in Phys Lett B 676:188–192, 2009). 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 Husung et al. (Phys Lett B 829:137069, 2022).

The original online version of this article was revised to correct the HTML version of equation ${min}_{i} {\hat{Γ}}_{i} ≳ - 0.3$ $\min _i\hat{\Gamma }_i\gtrsim -0.3$ if $N_{f} \leq 4$ $N_{\textrm{f}}\le 4$ .

An erratum to this article is available online at https://doi.org/10.1140/epjc/s10052-023-11392-3.

Copyright comment corrected publication 2023

Erratum to this article: https://doi.org/10.1140/epjc/s10052-023-11392-3

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Funded by SCOAP³. SCOAP³ supports the goals of the International Year of Basic Sciences for Sustainable Development.

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Logarithmic corrections to O(a) and O(a2) effects in lattice QCD with Wilson or Ginsparg–Wilson quarks

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