Eur. Phys. J. Plus (2015) 130: 229
https://doi.org/10.1140/epjp/i2015-15229-7

Regular Article

Influence of topology on the scale setting

¹ Universität Bern, Institut für Theoretische Physik, Sidlerstr. 5, CH-3012, Bern, Switzerland
² Deutsches Elektronen-Synchrotron DESY, Notkestr. 85, D-22603, Hamburg, Germany
³ Universität Münster, Institut für Theoretische Physik, Wilhelm-Klemm-Str. 9, D-48149, Münster, Germany

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

Received: 9 February 2015
Accepted: 9 October 2015
Published online: 19 November 2015

Abstract

Recently a new method to set the scale in lattice gauge theories, based on the gradient flow generated by the Wilson action, has been proposed, and the systematic errors of the new scales t₀ and w₀ have been investigated by various groups. The Wilson flow provides also an interesting alternative smoothing procedure particularly useful for the measurement of the topological charge as a pure gluonic observable. We show the viability of this method for supersymmetric Yang-Mills theory by analysing the configurations produced by the DESY-Muenster Collaboration. The relation between the scale and the topological charge has been investigated showing a strong correlation. We have found that the scale has a linear dependence on the topological charge, the slope of which increases decreasing the volume and the gluino mass. Moreover we have investigated this dependence as a function of the reference parameter used to define the scale: the tuning of this parameter turns out to be fundamental for a more reliable scale setting. Similar conclusions hold for the Sommer parameter r₀.