Non-perturbative determination of improvement coefficients and and normalisation factor with Wilson fermions - ALPHA Collaboration

Giulia Maria de Divitiis; Patrick Fritzsch; Jochen Heitger; Carl Christian Köster; Simon Kuberski; Anastassios Vladikas

doi:10.1140/epjc/s10052-019-7287-1

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2023 Impact factor 4.2

Particles and Fields

Open Access

Eur. Phys. J. C (2019) 79: 797
https://doi.org/10.1140/epjc/s10052-019-7287-1

Regular Article - Theoretical Physics

Non-perturbative determination of improvement coefficients $b_\mathrm{m}$ and $b_\mathrm{A}-b_\mathrm{P}$ and normalisation factor $Z_\mathrm{m}Z_\mathrm{P}/Z_\mathrm{A}$ with $N_\mathrm{f}= 3$ Wilson fermions

ALPHA Collaboration

Giulia Maria de Divitiis¹^,2, Patrick Fritzsch³, Jochen Heitger⁴^*, Carl Christian Köster⁴, Simon Kuberski⁴ and Anastassios Vladikas²

¹ Dipartimento di Fisica, Università di Roma “Tor Vergata”, Via della Ricerca Scientifica 1, 00133, Rome, Italy
² INFN, “Rome Tor Vergata” Division, c/o Dipartimento di Fisica, Via della Ricerca Scientifica 1, 00133, Rome, Italy
³ Theoretical Physics Department, CERN, 1211, Geneva 23, Switzerland
⁴ Institut für Theoretische Physik, Westfälische Wilhelms-Universität Münster, Wilhelm-Klemm-Straße 9, 48149, Münster, Germany

^* e-mail: heitger@uni-muenster.de

Received: 14 June 2019
Accepted: 6 September 2019
Published online: 25 September 2019

Abstract

We determine non-perturbatively the normalisation parameter $Z_\mathrm{m}Z_\mathrm{P}/Z_\mathrm{A}$ as well as the Symanzik coefficients $b_\mathrm{m}$ and $b_\mathrm{A}-b_\mathrm{P}$ , required in $\mathrm{O}(a)$ improved quark mass renormalisation with Wilson fermions. The strategy underlying their computation involves simulations in $N_\mathrm{f}=3$ QCD with $\mathrm{O}(a)$ improved massless sea and non-degenerate valence quarks in the finite-volume Schrödinger functional scheme. Our results, which cover the typical gauge coupling range of large-volume $N_\mathrm{f}=2+1$ QCD simulations with Wilson fermions at lattice spacings below $0.1\,\mathrm{fm}$ , are of particular use for the non-perturbative calculation of $\mathrm{O}(a)$ improved renormalised quark masses.