Ratio of flavour non-singlet and singlet scalar density renormalisation parameters in QCD with Wilson quarks - ALPHA Collaboration

Jochen Heitger; Fabian Joswig; Pia L. J. Petrak; Anastassios Vladikas

doi:10.1140/epjc/s10052-021-09387-z

2024 Impact factor 4.8

Particles and Fields

Open Access

This article has an erratum: [https://doi.org/10.1140/epjc/s10052-021-09924-w]

Eur. Phys. J. C (2021) 81: 606
https://doi.org/10.1140/epjc/s10052-021-09387-z

Regular Article - Theoretical Physics

Ratio of flavour non-singlet and singlet scalar density renormalisation parameters in $N_{f} = 3$ $N_\mathrm {f}=3$ QCD with Wilson quarks

ALPHA Collaboration

Jochen Heitger¹, Fabian Joswig¹, Pia L. J. Petrak¹^c and Anastassios Vladikas²

¹ Institut für Theoretische Physik, Westfälische Wilhelms-Universität Münster, Wilhelm-Klemm-Straße 9, 48149, Münster, Germany
² “Rome Tor Vergata” Division, c/o Dipartimento di Fisica, INFN, Via della Ricerca Scientifica 1, 00133, Rome, Italy

^c p_petr04@uni-muenster.de

Received: 18 February 2021
Accepted: 27 June 2021
Published online: 13 July 2021

Abstract

We determine non-perturbatively the normalisation factor $r_{m} \equiv Z_{S} / Z_{S}^{0}$ $r_{\mathrm{m}}\equiv Z_{\mathrm{S}}/Z_{\mathrm{S}}^{0}$ , where $Z_{S}$ $Z_{\mathrm{S}}$ and $Z_{S}^{0}$ $Z_{\mathrm{S}}^{0}$ are the renormalisation parameters of the flavour non-singlet and singlet scalar densities, respectively. This quantity is required in the computation of quark masses with Wilson fermions and for instance the renormalisation of nucleon matrix elements of scalar densities. Our calculation involves simulations of finite-volume lattice QCD with the tree-level Symanzik-improved gauge action, $N_{f} = 3$ $N_{\mathrm{f}}= 3$ mass-degenerate $O (a)$ ${\mathrm{O}}(a)$ improved Wilson fermions and Schrödinger functional boundary conditions. The slope of the current quark mass, as a function of the subtracted Wilson quark mass is extracted both in a unitary setup (where nearly chiral valence and sea quark masses are degenerate) and in a non-unitary setup (where all valence flavours are chiral and the sea quark masses are small). These slopes are then combined with $Z \equiv Z_{P} / (Z_{S} Z_{A})$ $Z \equiv Z_{\mathrm{P}}/(Z_{\mathrm{S}}Z_{\mathrm{A}})$ in order to obtain $r_{m}$ $r_{\mathrm{m}}$ . A novel chiral Ward identity is employed for the calculation of the normalisation factor Z. Our results cover the range of gauge couplings corresponding to lattice spacings below $0.1$ $0.1\,$ fm, for which $N_{f} = 2 + 1$ $N_{\mathrm{f}}= 2+1$ QCD simulations in large volumes with the same lattice action are typically performed.

The original online version of this article was revised: equations (5.5b) and (5.5c) were not correct. The original article has been corrected.

An erratum to this article is available online at https://doi.org/10.1140/epjc/s10052-021-09924-w.

Copyright comment corrected publication 2021

Erratum to this article: https://doi.org/10.1140/epjc/s10052-021-09924-w

© The Author(s) 2021. corrected publication 2021

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